Mathematical Olympiad | Algebra Problem | Math Olympiad Preparation
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- Опубліковано 6 жов 2024
- Can you solve the given rational and exponential equation for x?
Today I will teach you tips and tricks to solve the given olympiad math question in a simple and easy way. Learn how to prepare for Math Olympiad fast!
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Mathematical Olympiad | Algebra Problem | Math Olympiad Preparation
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Nice problem and solution. I got through the first part of step one (factoring the coefficients) then tried to split the fraction by the common denominator, but got stuck. I was trying to eliminate 3^x7^x from the denominator, and got into a trap. Factoring the sum of cubes in the numerator was the missing piece. 👍
Thank you for your Nice feedback! Cheers!
You are awesome 😀
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let
3/7= u
not
(3/7);x =u
Nice problem! So patient of you to go through all the steps for students who need them.
I like to reduce the clutter early by substituting for 3^x and 7^x.
Your key insight is to focus on the LHS first, factor and then divide top by bottom, giving a quadratic.
Great point!
Thank you for your feedback! Cheers!
You are awesome, Chandler 😀
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The Guru,you always inspires me.It's joy to watch!
Math is so easy with your step by step tutorial.How fantastic you are!
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تمرين جميل رائع حقا . شكرا جزيلا لكم. والله يحفظكم ويرعاكم ويحميكم . تحياتنا لكم من غزة فلسطين .
As you factored the u expression, i realised the answers, which one could see as obvious if you just add the numerator and denomenator. takes 5 seconds of mental arithmatic or 5 mins of algebra - very good!
Very nice!
I completed the cube in the numerator, by adding and subtracting three times the denominator from the numerator, leading to the same quadratic with roughly the same work.
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the first time when I saw this problem, I thought the value of x was 1 😂
U correct kayan
Nice to meet you again! Yesterday your comments were switched off. Thank you for a nice task and a good detailed explanation as always. God bless you, sir!
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Thanks for drawing my brain along into a nice orderly solution.
Herr professor, here there is only one value for X, ONE
Hugs from a Brazilian who loves math!
Sir, can we simply your Step - 2: which reads (u-1+(1/u)) = (37/21) in another simple way for solving 'u' such as this? We can now write Step - 2 as (u+(1/u)) = (37/21)+1 = 58/21. Using the algebraical identity (a - b)^2 = (a + b )^2 - 4ab, considering u = a and (1/u) as b, now {u - 1(/u)}^2 = { u + (1/u)}^2 - 4.u. (1/u) which becomes on simplifying, = (58/21)^2 - 4= (40/21)^2. So that u - (1/u) = +/- 40/21 (have two values). Let us consider + sign of u. We have u + (1/u) = 58/21 and u - (1/u) = 40/21. Therefore from this, u = (1/2){(58/21)+ (40/21)} = (1/2).(98/21) = 49/21 = 7/3 = (3/7)^-1. Now putting the value of u we get (3/7)^x = (3/7)^-1. So that x = -1 (one result). Taking the other (negative) value of u as - (40/21), we have u + (1/u) = 58/21 and u - (1/u) = - (40/21) so that u becomes = (1/2){(58-40)/21 }= 9/21 = 3/7. Putting the value of u, (3/7)^x = (3/7). So that x = 1. Therefore x = +1 and also -1.
A really simple problem presented so wittily. Perfect for JEE/ MBA entrance examinations. Brilliant.
I wonder, why math becomes so easy with your explanation.
Waitung for others
Another elegant solution. Very encouraging. Thank you
good explanation. but for instance we can do fast solution = 27+347= 370 and 63+147 = 210. so 37^x/27^x = 37/27====> x=1
Nice solution!
My working is far, far simpler than that given. At an early stage put a = 3^x and b=7^x and rewrite the equation, factorizing both top and bottom, seeing the common factor (a+b) and confidently cancelling as you know it can't be zero because then the expression would come to 1 and it isn't. Then the numerator shows that (3x7)^x = 21 so x = 1 is the obvious choice, which makes the numerator 37. Done.
Very very intriguing way to solve it! a question: I get used to see how many solution a generic equations has, seeing the grade of the x into the equation itself. But, in this case, why there are two solutions if the original equation seems to have only a grade of 1? Why it seems hidden this time so there, and in reality, are two solutions?
I didn't see the sum of cubes, so I need to brush up on this stuff.
However, x = 1 is the obvious solution since
27 + 343 = 370 and 63 + 147 = 210.
Thank you for your feedback! Cheers!
You are awesome, Hans 😀
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Like 341
Nice sharing sir. Your way of teaching is so easy to understand... thanks for sharing very helpful video...👍👍👍
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12:00 have you heard of synthetic devision? it is very fast and easy
🙏🏻 proffessor sir sharing reply x=1,-1
Excellent!
Thank you for your feedback! Cheers!
You are awesome, Kalyan 😀
Divido N e D per 7^3x*3^3x....risulta dopo lunghi ma semplici calcoli x=1,-1
Как можно раньше нужно сократить дробь на 7^3х или на 3^3х и сразу сделать замену переменной. Будет то же самое, но гораздо-гораздо удобнее.
Nice ! Solution îs manipulation 3 and 7
At first glance, x=1 is a solution because 27+342 =370 and 63+147=210, so 370/210 équals the LHS.
Solving the equation is easy. What I am wondering is who and how to invent this equation.
I notice there's not the usual huge crowd of people explaining how THEY did it! Just a few this time.
Much simple solution is possible
Nice problem and good solution!
the answer is x-1, solve it using try and chec strategy.
Bravo!
Amazing
I love your content. Any Biology and Agriculture problem can be channelled to The Eagle TV for assistance. Thank you❤
master class!!!
Very nice step by step tutorial👍👍
😋 Thanks for sharing
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Excellent explained 👍
Just take x as 1 and you will get the same rhs as if you take any value to x the answer will always come the same
V nice
So nice of you.
Thank you for your feedback! Cheers!
You are awesome, Niru 😀
@@PreMath Sir you go to the minutest detail with so much patience🙏🙏
Good problem to review and get your hands dirty with algebra.
Good point!
Thank you for your feedback! Cheers!
You are awesome, DJT 😀
great job
Glad to hear that!
Thank you for your feedback! Cheers!
You are awesome, Nico 😀
cool elegent answer
thanks😀
What happened to the 3 power 2 in the denominator?
x=1
i solve it successfully
Nice explanation
Thanks for liking
Cheers!
You are awesome, Susen 😀
actually the value of x is nothing in my life because I don't have any x
Beautiful
370/210 = 37/21
Very Simple ans : x = 1
-1 works as well
My eyes ouch ... use a black background please 🙏
román to number
5th comment
Thanks! Cheers!
You are awesome 😀
E
好，奖 1 万元
Prays Jesus Christ Holy Bible (Matt 4:17) From that time on Jesus Began to preach, "Repent, for the kingdom of heaven is near." Prays Jesus Christ. Amen. Hallelujah.2022.
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37÷21=1.761904
4th comment
Thanks Jayant