Can You Pass Harvard University Math Exam?
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- Опубліковано 8 вер 2024
- What do you think about this question? If you're reading this ❤️. Have a great day!
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@higher_mathematics
#maths #math
X=3. It's mental arithmetic
I solved it with only seeing the thumbnail and the video is 14 minutes 😂
Me too bro
idem
8 vi class ka h squares & cubes aana chahiye
Same 😂
yeah, me too
ok but 3^x=x=30 => 3^x+x=27+3 => 3^x+x=3^3+3 ==> x=3 easy
3ˣ+3=3³+3
3ˣ+3=3³+3
-3 -3
..................
3ˣ = 3³
ln3ˣ = ln3³
x ln3 = 3 ln3
x ln3 = 3 ln3
--- ---
ln3 ln3
x = 3
Knowing is not the same as proving.
Fake
Everything this channel does seems to be about lambda-W function. We need a little more variety please.
@@Taozilin yes but you need to do it in the "hard" way or else the test graders in Harvard won't take you srsly.
Just put x = 3 by hit and trial method!
My advice as a 10th grader.
Certified chtya 😂😂 , beta vo Harvard h . Tumhare IIT se 1000x better . Sorry , tumhare 10th ke 🤡 result se 1000000x better.
Oh thats so smart .......bro if u get a question to prove that it is a triangle just for example will you say the same thing there also?? Or will you prove it
@@user-so4ol2xl9nHarvard question is mcq type so you don't have to prove:)
nah nah nah if the Value of x Is 3 thn the Equation should look like this - 3x3 +3 = 30
or solve it 9+3=30
No sense
@@CHEEKU_GAMER123 le me guess you are just a 7th grade student right?.......in equation its 3 to the power x not 3*x
7 class students solving it in mind
Got it in seconds 😂
nah nah nah if the Value of x Is 3 thn the Equation should look like this - 3x3 +3 = 30
or solve it 9+3=30
No sense
@@CHEEKU_GAMER123 bro it isn't (3x3) its (3³) => 3 × 3 × 3 = 27
27 + 3 = 30
@@SaquariusGaming My bad I didn't saw it was power
Some of the commenters are silly passing themselves off as genii. It is the method that counts not the simple solutions, or trial and error, or solving by spotting the 3 factor.
The poster is passing the question off as a Harvard University math exam. It's the same misrepresentation every day. Why you would call out UA-cam browsers who happen to state that they can see a real root, is beyond me. Why do you hold them to a standard of mathematical prowess, when they require none? It seems stranger still that you don't hold the poster to a standard of intellectual integrity, while they bait views with false claims.
@@davidnewell3232its the concept that matters to me personally, even though i solved it from the thumbnail, i was puzzled on how you would solve it normally with theory
Without any thinking I had solve this easily by guessing concept of class 6
Put, x = 3
then, 3³ + 3 = 30
27 + 3 = 30
∴ x = 3 ans
I'm by no means a math genius, but it was explained so well that even I understood the solution, thanks, you saved an otherwise boring evening for me (it's now evening in Germany)
1) If x < 0 then 30 = (1/3)^|x| - |x| < (1/3)^|x| < 30 : contradiction, so there is no negative solution.
2) x=0 is not a solution
3) f(x) = 3^x +x - 30 increases strictly in (0,+ infinity), so f has at most one zero (i.e. there is at most one solution)
4) x = 3 is a solution.
Conclusion : 3 is the only solution of the equation in R.
At 10 min, rewriting 3^30 as 27×3^27 is equivalent to guessing the answer to 3^x = 30-x, which is guessing the answer to the original question. This is like giving a complicated procedure for fixing a car where step 10 is "take it to a mechanic".
I do enjoy your videos, though. Your voice is very relaxing.
Uhm... I just wrote a comment saying exactly that. And then I read yours. You were first. You are right. He only can factor out 3^3 * ln 3 * 3^27 if he KNOWS 30-x = 27. And you don't need the Lambert function at all. Actualle he does not even use it to calculate the value for W().
While it IS true that you use the Lambert W functions to solve equations of this form, that is not how it is done here. Actually you don't need the Lambert function at all. Because he does not ever calculate the value for W_0(x). He only puts the Lambert function on both sides of the equal sign to show that W(p) = W(q). At 09:42 he shows that 3^30 * ln3 = 3^3 * 3^27 ln 3. So how does he know that? Why not 3^4 * 3 * 26 ln 3. You can ONLY do this when you know what to expect, namely 30-x = 27. And that is exactly the same as guessing that x=3. And you totally DO NOT need that Lambert function to come to this. Although it is a nice way to simplify the derivation. You just have to skip the step that W(x*e^x) = x. Since you do that on both side of the equal sign you might as well omit it.
I don’t think it’s based on knowing 30 - x = 27.
Example, if I saw W(4^260 x ln4), then I would think about different exponents of 4 to rework the expression. Since 4^4 = 256, this could be rewritten as W(4^4 x 4^256 x ln4) or W(256ln4 x 4^256). Following the additional steps will then make it possible to solve Lambert W.
Who are successfully calculate this answer in brain 🔥👽💫🙌
Lets break 30
27+3 = 3'x +x
3*3*3+3 =3'x +x
3'3 + 3 = 3'x + x
x= 3
Why giving a simple answer when the complicated one is so beautiful.
В левой части - монотонно возрастающая функция,в правой - константа. Следовательно, уравнение имеет не более одного корня . Очевидно,что х=3 - корень. Вот и всё.
This sum is solvable just from thumbnail
did it really need to be that complicated.
if we find that x=3 is a solution then since x and 3^x are monotonic increasing which proves that x=3 is unique.
using your method could we find the solution to x+3^x = k where k is some other number than 30
i was teaching calculus to the engineering students integrations, derivations, differential equations, (and solvings) laplace and frouier transformations, rotation gradient nabla operators, etc.. many years ago (more than 45y .But now i cant remember W function right now..Can you explain breafly?
That was the same thing I thought. I am not teacher, only a graduated engineer. In 1983. Never heard of the "Lumber double the function" . It seems to be Lambert W function. Which I think is somewhat far fetched for this solution. But then I again I am no Harvard student.
Thankyou Brother ! I am loking for this type of question and you provide this with good explantion .
Love form India ❤
3 is a trap, guys. The point is, why should it be 3 and not something else, especially when you have no intuition?
A monotonic function or something like that might exclude other possibilities once you have 3 as the answer, but you arrived at 3 based on intuition.
Your pfp checks out with this comment of yours
Super elegant and interesting solution using w function.
Its too long you can just put value by guessing and get the answer tho😂
f(x)=3^x+x is monotone and increasing. Hence, the graphs of f(x)=3^x+x and y=30 intersect once. An obvious solution is x=3. There are no other solutions in real numbers.
I was funding such a math . THANK 🎉YOU SO MUCH.
I think a more helpful way to present this method would be to show the given equation, demonstrate how easy it is to figure out, then mess it up with numbers that don't solve easily. What do we do now?
Thus we would need a generalized approach to problems like this. In to save the day is the Lambert W function.
I'm from "Old School" learning, and simple expressions like this should be first looked by trying solutions of 0, 1, 2 or 3.
And guess what --- 3 works.
just take x common and break 30 = 3*10, from observations x =3. If you dont believe then simply put value of x in the equation you made by taking x common and you will get 30
A beautiful and very clear explanation.
I was struggling with this for a while; then I put the video on, and after hearing the step “divide by 3^x” it finally clicked, and I was able to solve it from then on. Great video and explanation as always.
Cant you take derivative amd motice its increasing, thefore only has one solution? x=3 is really easy to guess
,,,,i know,,But how did 3 come, this thing is difficult to solve.
Just by guessing i did the same @@Arunmourya.123
And get 0.5 marks.
@@noelinx what is the mistake though?
@@hmkl6813 0.5/5 as it's too short, if we do it directly. But for questions like 5^x + x = 30.. this brute force approach will not work.
Very nice, however - you didn't really applied W function. I mean - you didn't really compute it, nor read from tables. Only to compare both sides.
So it should be possible to solve with another compare trick.
3 works which is nice for a times test, but the Algebra was "good fun" & math practice...
Ans 3 as
Atp
3^x + x = 30
3^x + x = 27 + 3
3^x + x = 3^3 + 3
So,x=3
Obviously, x=3 is solution, but ,if x 3^x+3>30
the real thing is proving the equation. therefore this video is really helpful and btw those who are saying i solved it in my head, I know its easy but the real thing is proving and showing how.
Zio, sei andato a scomodare la funzione di Lambert W quando l'equazione è di facile risoluzione
Good,if they need the solution to the question,but this can be done easily without that many steps
X=3 simple just by seeing
There must be an easier way. I also wonder if this was the way Harvard intended it. I agree that inspection does not show why.
Because students think it has some hard calculus question but it just some simple question
3^x=x=30 => 3^x+x=27+3 => 3^x+x=3^3+3 ==> x=3 easy
@@andregomes554 no some times x can be in decimel,irrational and imaginary
Thats very easy...i challenge anyone here to try JEE Advanced Question
I just solve this within few second
Give me Harvard certificate....
Quick...
Guys this is not meant for any method like hit and trial guess if the question answer is a 4 digit number will you try all number this is a concept based question at easy level its concept is hard but the question is one of the easiest from the concept so pls dont think it
bro speaks in one breath
At a quick glance 3^3 = 27 then 27 + 3 = 30 and x = 3.
The problem is trivial. x=3 by inspection and there are no other real solutions. Meh.
People thinking they are smart until they are told to do it by process
Welcome to Lower Mathematics youtube channel 😂😂
Me before the video: this better not be another Lambert W function
Me right in 3 minutes: of course
difficulty level-American
This Lambert function is very useful.
easy question , i don't see why it would be in an ivy Legue school exam
Brother it hardly took 5 seconds to think the answer is 3
Us 😂
There is something called hit and trial method
Which i used to slove it 😂😂
Answer is 3.Bruh i solved it in 6 seconds this ain't no Harvard question please.
Solve this if you can (16/x)^x=256
this is the reason why I use trial and error😅
It took 3 sec to figure the answer that very easy
This is quite easy for me being a seventh grader
Se ad un esame mi presenti una soluzione di questo tipo per un esercizio così semplice prima ti boccio poi ti faccio volare fuori dall'aula. Questa non è matematica! Più sono corte le soluzioni e le dimostrazioni più sono eleganti e meno si corre il pericolo di sbagliare. Il voto d'esame dovrebbe essere composto da 2 parti: 1) risultato corretto, 2) metodo di risoluzione.
a^x + x = b
x = b -(w(a^b • ln a))/ln a
3^x + x = 30
x = 30 -(w(3^30 • ln 3))/ ln 3
= 30 -(w(27ln 3 • 3^27))/ln 3
= 30 -(w(27ln 3 • e^(27ln 3)))/ln 3
= 30 -(27ln 3)/ln 3
= 30-27
x = 3 ***
I thought it'll be some trick but I just got the answer just after writing the question down
I just looked at it and figured it out in like 2secs. I mean 3^3 is 27 and 27+3 is just so happens to be 30
so you study in Havard?
@@jenshagelstein7695 is that suppose to be sarcasm?
@@andrasnoll2559Even if it is, take it as a compliment somehow.. 😂
Substitute x value it takes only 2 min 😂😂 for that 14min they took
X=3 clearly by observing 😅
Simple exponential arithmetical Sum
And linear equation
X =3 very easy for indian
I totally dont know what to write if this was an essay 😂
No way im gonna write 'try 1, 2 or 3' on the paper😂
I can solve by mind but not using page 😂
It's all about observation 😂
Ye, in one step. X = 3.
Please make a video solving 2 power x + x = 5
Hit and trial answer in a minute 🤣🤣🤣🤣
X=3
Inn just 1.35 second
Solved it in first 3 seconds,IIT jee things...
Bro if you see their is one more solution to it and you need to find it out either using log or graph
Jee advanced laughing at corner😂
I have one idea😂
3^x+x=30
Therefore3^x+x=3^3+3
X=3
Heard about lambda w function for the second time and now I fairly know where I heard it the first time. Who created this function 😂?
3x +x=3³ +3
X=3
3^x + x = 30 = 3
Just go on petting x=1, 2, 3...etc.
3 will satisfy the equation. So x=3 is solution. This is trial and error method. Easy
Very nice, very clever. 👍
Why do it simple if you can do it complicate.
I saw it without any kind of math.It is 3
I just calculated it in my mind
X=3
I solved it in 10 seconds
30=27+3=3^3 +3 ===>x=3🙃
Ans 3 am I going to havard university 😃
congrats!! harvard is waiting 4 u
X=3.
Anything else ?
Obviously it’s an ever increasing function so there is no other solution.
Its not a function... its an undefined function.
But depends if you believe undefined functions are also functions.
Harvard ?? Bruh compare it to parayana and free chaitanya in India bruh
Try jee ADVANCED questions
Why do you have to solve it so long
Like 14min ..
Bruh.. I solve it in 3 sec
Do we have to write solutions also or only MCQs??
Is this really harvard question
what's about multiply all to the log in base x ?
X=3 easy
thumbnail solution within 10 sec nikal diya its 3
For what is this needes in life?
I solved in the thumbnail it self mcq hota tho 10 seconds lagta basd and prove karne bolta tho me ye question chorr deta