By inspection m is - 3. Use synthetic division to get the other factor with (x+3) as one factor. Use the quadratic formula to get the other 2 roots. Simple, straight forward and easy. Thanks. 😢
The difference between a square and a number of cubs is positive. It implies the number is negative. m = - 3 whose square and cubs satisfy the condition.
@ what you say is correct, however it’s presented as a University entrance problem. It isn’t, it’s a very early problem on solving higher order equations. There is simply no need to intimidate people watching to learn by producing lengthy algebra solutions which aren’t necessary.
@ stating the obvious? I could just plug numbers in like a trained monkey and that would eventually solve the problem. The truth is, a solution is BETTER when it is simpler and fast. Running through an algebraic humdrum like done here is a complete waste of time. And then the attitude that went along with that solution was wrong. STEM is not a club for which only some get to be a part. Everyone who likes to think gets to join. Choose a non-stem field if you can’t do this? That’s crap. This guy shouldn’t be in a STEM field.
Instead of just using inspection to find -3 as a solution as some other commentors have suggested, consider the following: First of all, we look for an integer solution. Factoring the LHS we get m^2 (1-m) = 36 Consider now how 36 can be factored into a perfect square (m^2) and another integer (1-m): 36*1 or 9*4 or 4*9 or 1*36. So we have the 4 cases: (Case 1) m^2 = 36 and 1-m = 1 hence m = 6 or -6, while m=0 (a contradiction) (Case 2) m^2 = 9 and 1-m = 4 hence m = 3 or -3 while m=-3 ( m=-3 is a SOLUTION) (Case 3) m^2 = 4 and 1-m = 9 hence m = 2 or -2 while m=-8 (a contradiction) (Case 4) m^2 = 1 and 1-m = 36 hence m = 1 or -1 while m=-35 (a contradiction) Now with m=-3 as a solution, we know m+3 is a factor of the polynomial m^3-m^2+36 so by division we can get m^2-4m+12 as the other factor - then the Quadratic Formula will give us the other two (complex) solutions to our problem.
We are not on the same level.......a lot still need some basic explanation, nevertheless, we appreciate ur observation. it is already taken in over the subsequent videos. We love u all.
Exactly. It's not the answer that's the problem here, it's the question, good teachers don't set questions that can easily be guessed then spend 20 minutes doing it a 'long' way, it invites comments and attitudes like this. Why bother?
Everyone is not at the same level in Mathematics.......therefore we have to mention every basic rule, explain every dime, go to the root as much as u can, that is why
équation du 3eme degré donc 3 racines (solutions) dans cette équations 1racine réelle et 2 complexes je crois me souvenir qu'il existe des relations générales donnant les solutions pour l'équation du troisième degré et pas pour les degrés supérieurs
Initial observations:: Although it's not specified, usually the variables m and n are used for integer, not general real numbers. Clearly m must be a negative number. Trying a few small values, it's clear that -3 works. Are there any other solutions? At this point I just watched the video.
Sometimes, we guess right when the answer is WHOLE NUMBER, what if the answer is decimal, fraction, irrational number etc. While guessing is brilliant, which is part of math.....it is also advisable to understand the actual process of solving a problem.
This was not a guess. It was analysis. 1: factorise both sides to see into the mathematical structure of the formulation 2: note that both sides then contain a repeated term. 3: test what happens if these two squares are presumed equal and discover the answer. It is not “guessing”. It is “insight” into the structure of the question. If you don’t like that, don’t set a question for which the answer is so easily found.
simply it can be told that no imaginary number while in square root we got imaginary number having negative sign. no need for carrying out such a long calculations afterwards
By inspection? What kind if an answer is that? So lazy. If the number on the left was not 36, say 35. Inspection will not work. Brobably logs at that point.
You spend too much time on several trivial steps that are unnecessary. People who follow this type of video, know and understand these trivial steps. Walter Wen and Prolisine give more elegant solutions in their comments. Dr. Ajit Thakur (USA).
We are not on the same level.......a lot still need some basic explanation, nevertheless, we appreciate ur observation. it is already taken in over the subsequent videos. We love u al
@@SchoolClassMath It is the only way to get a positive with a square and a negative with cubic, when you do the numbers it adds. You can also have m square as a common factor multiplied in parenthesis by 1 - m. m has to be negative of value equal 3
🤣😆🤣🤣 anyone tried to solve this the way presented will NEVER get to Harvard. This is tops a 5 seconds solution you can do in your head, this is how these questions are designed, to test your common sense. U sir have ZERO common sense
By inspection m is - 3. Use synthetic division to get the other factor with (x+3) as one factor. Use the quadratic formula to get the other 2 roots. Simple, straight forward and easy. Thanks. 😢
Good observation
@@sivanaidoo5602, k
Ok
@@sivanaidoo5602 it’s easier than this.
The difference between a square and a number of cubs is positive. It implies the number is negative. m = - 3 whose square and cubs satisfy the condition.
Nice
Trivial problem. -3 by inspection. Then m^3-m^2+36=0. Divide lhs by x+3. Solve.
If it takes 20 min consider a non science degree.
Good observation
if you have to do it this way, consider a non-science degree. lol
You guys are too much😂😂😂 he was showing the entire picture of course they're faster ways to do it 😂😂😂
@well now that you have the answers in the various responses, you say that. Lol. I love how you guys love stating the obvious.
@ what you say is correct, however it’s presented as a University entrance problem. It isn’t, it’s a very early problem on solving higher order equations. There is simply no need to intimidate people watching to learn by producing lengthy algebra solutions which aren’t necessary.
Very well explained with no steps omitted and easy to follow every stage.
Thanks, really appreciated
easy: factor left side
m²(1 − m) = 36
then, since 36 and m² are positive, 1 − m must be positive so m < 0, then m must be -3 since (-3)² (1 − -3) = 36
Many ways of solving math problem
@ stating the obvious? I could just plug numbers in like a trained monkey and that would eventually solve the problem. The truth is, a solution is BETTER when it is simpler and fast. Running through an algebraic humdrum like done here is a complete waste of time. And then the attitude that went along with that solution was wrong. STEM is not a club for which only some get to be a part. Everyone who likes to think gets to join. Choose a non-stem field if you can’t do this? That’s crap. This guy shouldn’t be in a STEM field.
@@oidbio2565 But you have two additional complex roots, which isn't so easy to find, if you don''t remember advanced algebra well.
Students will sleep if they listen to your explanation
People's learning rates are not the same
Instead of just using inspection to find -3 as a solution as some other commentors have suggested, consider the following:
First of all, we look for an integer solution.
Factoring the LHS we get m^2 (1-m) = 36
Consider now how 36 can be factored into a perfect square (m^2) and another integer (1-m):
36*1 or 9*4 or 4*9 or 1*36.
So we have the 4 cases:
(Case 1) m^2 = 36 and 1-m = 1 hence m = 6 or -6, while m=0 (a contradiction)
(Case 2) m^2 = 9 and 1-m = 4 hence m = 3 or -3 while m=-3 ( m=-3 is a SOLUTION)
(Case 3) m^2 = 4 and 1-m = 9 hence m = 2 or -2 while m=-8 (a contradiction)
(Case 4) m^2 = 1 and 1-m = 36 hence m = 1 or -1 while m=-35 (a contradiction)
Now with m=-3 as a solution, we know m+3 is a factor of the polynomial m^3-m^2+36 so by division we can get m^2-4m+12 as the other factor - then the Quadratic Formula will give us the other two (complex) solutions to our problem.
Good idea
m1=-3
m2=a-b
m3=a+b
m^3-m^2+36=0
m1+m2+m3= 1
-3+a-b+a+b= 1
2a=4
a=2
m1*m2*m3= -36
-3(a-b)(a+b)=-36
a^2-b^2=12
4-b^2=12
b^2=4-12=-8
b=2isqrt(2) or b=-2isqrt(2)
20 minutes?! Ridiculous
We are not on the same level.......a lot still need some basic explanation, nevertheless, we appreciate ur observation. it is already taken in over the subsequent videos. We love u all.
😮
Wow. I was working through, but need 2 sheets of paper.
Took me about ten seconds to recognize that m needed to be a negative number and then another 10 seconds to get to negative 3
What if m is a decimal, fraction, or irrational number ?
Exactly. It's not the answer that's the problem here, it's the question, good teachers don't set questions that can easily be guessed then spend 20 minutes doing it a 'long' way, it invites comments and attitudes like this. Why bother?
Everyone is not at the same level in Mathematics.......therefore we have to mention every basic rule, explain every dime, go to the root as much as u can, that is why
His yellow explanation section is a brilliant idea
Thanks
Holy crap! i just looked at it and in 15 seconds on quick substitution had it.
U mean ?
I use method parcial of derivates.
F(x) - m^3 = - 3m^2
m^2 - 3m^2 = - m^2
F'(x)- m^2 = - 2m
- 2m = 36
m = 36 / - 2
m = - 18
🤦♂️ if m = -18, m^2 - m^3 equals 6156
"m^2 - 3m^2 = - m^2"
And also, this is incorrect: 'm^2 - 3m^2 = - 2m^2".
lol
You probably have changed the question
there is no such exam at harvard univ
Зачем разжевывать и растягивать на 20 минут? Люди могут сами самостоятельно быстро найти корни квадратного уравнения.
I love to contribute......but the language
Есть же переводчик. Я со своей стороны в будущем постараюсь ипользовать более простые фразы которые можно перевести однозначно.
m2-m3=36
m2(1-m)=9*4
m2=9 => m=-3 or m=3
1-m=4 => m=-3
m=-3
Good observation
équation du 3eme degré donc 3 racines (solutions) dans cette équations 1racine réelle et 2 complexes
je crois me souvenir qu'il existe des relations générales donnant les solutions pour l'équation du troisième degré et pas pour les degrés supérieurs
m^3 -m^2 + 0m + 36 = 0
m^3 -m^2 + 0m + 36 divided by m+3 is
[m^3 + 3m^2 - 4^m^2 - 12m + 12m + 36]/(m+3) = m^2 -4m +12
so m = -3 or m = [4+-sqrt(16-48)]/2 = 2+-isqrt(36)/2 = 2+-3i
U are welcome
My POV one by observation and other two by theory of polynomial
Nice one
It always baffles me, how come any problem gets so easy after knowing the solution ?
Being at the simple end of the Dunning Krueger spectrum, that has always bothered me as well
That is the beauty of Mathematics...... bro
Steps are so difficult to follow and not helpful for stidents
The Channel is about making solution simple as much as possible
(-3)^2-(-3)^3=36.
9-(-27)=36. Hence the answer is m=-3.
Good observation
Your explanation and solution are easy to follow. Excellent!
Thank you.
Thanks so much
-3...that took ten seconds of simple logic
Yeah, that is absolutely right, but what if m is fraction, decimal, irrational number ?
Initial observations:: Although it's not specified, usually the variables m and n are used for integer, not general real numbers. Clearly m must be a negative number. Trying a few small values, it's clear that -3 works. Are there any other solutions? At this point I just watched the video.
Appreciated
m^2(1-m) = 36
But we note 36 = (3^2)(4)
and thus m must be -3
Sometimes, we guess right when the answer is WHOLE NUMBER, what if the answer is decimal, fraction, irrational number etc. While guessing is brilliant, which is part of math.....it is also advisable to understand the actual process of solving a problem.
This was not a guess. It was analysis.
1: factorise both sides to see into the mathematical structure of the formulation
2: note that both sides then contain a repeated term.
3: test what happens if these two squares are presumed equal and discover the answer.
It is not “guessing”. It is “insight” into the structure of the question.
If you don’t like that, don’t set a question for which the answer is so easily found.
Good observation
It is easy to guess -3.
Yeah, you are right, but what if the value of "m" is decimal fraction, any idea ?
-3,solved in 0.00001 second in mind
You mean ?
@SchoolClassMath It was very easy for me
I pray we are all operating at the same higher frequency
10x10 = 100
4x4x4 = 64
100-64 = 36
@@mathewtom6478 Observation
@@mathewtom6478 Observation
In my opinion it's faster using Horner method for polynomial. Why guessing a lot for 20 minutes?
Takes longer time to explain to slow learner
m should be equal to -3
m² -m³
(-3)² - (-3)³
= 9-(-27)
9+27=36
Therefore, m = -3
36=9+27
m²-9=m³+27
m-3=m²+9-3m
m²-4m+12=0
m=2±2√2i
or m=-3
m = -3
Audio balance/tuning is definitely not one of yr majors.
That is a brilliant observation except it is not one of the best of the year
Isn’t it just m=-3? Why waste so much pen and paper for something that’s staring you in the face?
Mathematics
@@SchoolClassMath You have to find the other two complex roots.
possibly in another video...Yeah
M^2-m^3 = 36 = 9 + 27
- or + ^2 always +
-^3 always -
As m^2 - m3 is impossible + with m +
So m must be - for 9 + 27 = 3^2 + 3^3
Then m = -3
Observation
Without any calculations I could see it was about a small value. First I tried with -2, then -3. And voilà!
It means you are a genius.... I welcome more ideas
m^2-m^3=36
=m^2-3=36
=1/m=36
1/m=36
m=1/36
Problems that seem boringly and insultingly obvious are still useful early practice for beginners though...
You might be right
simply it can be told that no imaginary number while in square root we got imaginary number having negative sign. no need for carrying out such a long calculations afterwards
What if the "m" is a decimal fraction, irrational number?....suggestion might not be the way out
It is -3 - by just looking at it
What if the value of "m" is decimal, fraction or irrational number ? inspection method might not bail out
m^2(1-m)=36
(-3)^2(1+3)=36
m=-3
Really
By inspection? What kind if an answer is that? So lazy. If the number on the left was not 36, say 35. Inspection will not work. Brobably logs at that point.
I love this!
A third degree equation m^2 (m-1)= 36 which has no rintegr real solution
Observation
m= -3 , m*m =9 , 1- m=4 4*9 =36
Yeah
Many WILL know. So what is your point?
My point ? If the value of "m" is a decimal fraction, what is going to be done...suggesting or guessing ?
@ then why state that many will not know? Why the negarivity?
Nice
Thanks
How many do not know the first step?
It is obvious that the number had to be negative.
Good observation
m = -3, you can see it right away.
You are not wrong
There is no entrance exam to Harvard.
I do not think this could be slowed down.
Yeah
Harvard University Entrance Exam: m² - m³; = 36; m =?
m² - m³ = 36. m² = 36 + m³ > 0; 36 > m² > m³ > 0
m² - m³ = 36 = (9)(4) = (9)(1 + 3) = 3² + 3³ = (- 3)² - (- 3)³; m = - 3
Find the missing two complex value roots by solving the cubic equation;
m³ - m² + 36 = 0, m + 3 is a factor of the equation,
(m³ - m² + 36)/(m + 3) = m² - 4m + 12 = 0, m² - 4m + 4 = (m - 2)² = - 8 = (i2√2)²
m - 2 = ± i2√2; m = 2 ± i2√2 = 2(1 ± i√2)
Answer check:
m = - 3: m² - m³ = 36; Confirmed as shown
m = 2(1 ± i√2), m² - 4m + 12 = 0, m² = 4m - 12
m² - m³ = m²(1 - m) = (4m - 12)(1 - m) = 4m - 12 - 4m² + 12m = 16m - 4m² - 12
= 16m - 4(4m - 12) - 12 = 48 - 12 = 36; Confirmed
Final answer:
m = - 3, Two complex value roots; x = 2(1 + i√2) or x = 2(1 - i√2)
m^3 is not > 0.
Really !
You spend too much time on several trivial steps that are unnecessary. People who follow this type of video, know and understand these trivial steps. Walter Wen and Prolisine give more elegant solutions in their comments. Dr. Ajit Thakur (USA).
We are not on the same level.......a lot still need some basic explanation, nevertheless, we appreciate ur observation. it is already taken in over the subsequent videos. We love u al
9 + 27 = 36 = (-3)² - (-3)³
Of course yes
Harvard University Entrance Exam? , so poor level really? ... I prefer to ask in a better University ...
This is NOT an ``exponential question". You talk too much, sir. This is a 5 min. problem for competent student. It requires 3 lines.
We need to remember that, all students are not in the same level (of understanding)... need to carry every one along ..... sign of a good teacher
How to turn an exciting subject into absolute boredom.
You mean ?
@@SchoolClassMath The slow pace and repetition🤮🤮🤮🤮
Check other videos......you going to see that, this has been checked. Thanks, for the good observation
m= -3
Yeah. that is correct
m=-3 or m=2(1+sqr(2)i) or m=2(1-sqr(2)i)
You mean ?
Note: Harvard University does not have an entrance exam. Certainly not one with math problems.
Hello
m^3 - m^2 +/- m +36 = 0 , (m+3)(m^2-4m+12)=0 , m= -3 , m^2-4m+12=0 , m=(4+/-V(16-48))/2 , m=(4+/-V(-32))/2 ,
1 3 m=(4+/-i*V(32))/2 , m=2+/-i*V8 ,
-4 -12 solu , m= -3 , 2+i*V8 , 2-i*V8 , test , (-3)^2-(-3)^3=9-(-27) , 9+27=36 , OK ,
12 36 = 0 , test with WA , (2+i*V8)^2-(2+i*V8)^3=36 , (2-i*V8)^2-(2-i*V8)^3=36 , OK ,
Really appreciate this, it's actually making us getting better
@@SchoolClassMath Thanks , yes, let's inquire about the various solutions.
-3 just read what it was posted on the video.
So your observation is ?
@@SchoolClassMath It is the only way to get a positive with a square and a negative with cubic, when you do the numbers it adds. You can also have m square as a common factor multiplied in parenthesis by 1 - m. m has to be negative of value equal 3
@@ggrape0 Good observation
m=-3.
Yeah, m = -3
Una solución real sera x = - 3
x =-3
9+27= 36 hence x= -3
Yeah
1001 definition
You mean ?
Hoc m= ---3 est, respondeo. 😅😊😂
respondeo ?
-3
It makes sense
Ok
Thanks
Took me 10 seconds😂
Shows u are smart
m^2 - m^3 = 36
m^3 - m^2 + 36 = 0
(m + 3)(m^2 - 4m + 12) = 0
m = -3, 2 +/- 2i✓2
Nice one
@@SchoolClassMath Thank you 🙂
1
U ar welcome
@SchoolClassMath o, k
go faster
@mauriziodavoli8644, we really appreciate ur comments........this has been improved on. CHECK more videos
🤣😆🤣🤣 anyone tried to solve this the way presented will NEVER get to Harvard.
This is tops a 5 seconds solution you can do in your head, this is how these questions are designed, to test your common sense.
U sir have ZERO common sense
Let's assume the value of "m" is a decimal fraction.....I need someone to show us how suggestions will work here ( just asking for advice) sir
Hears anotter Hauvatt eksem bropläm: Why do so many faceless maths vloggers have funny voices?
Really appreciate ur observation
Bery slow.
Need to consider slow learners too
🥱 I hope you are not a teacher.
Teacher for life
-3
Yeah, m = -3
m = -3
Good speed
-3
Exactly
-3
exactly