Mathematical Olympiad | Algebra Problem | Math Olympiad Preparation

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!
Step-by-step tutorial by PreMath.com
• Mathematical Olympiad ...
Need help with solving this Math Olympiad Question? You're in the right place!
I have over 20 years of experience teaching Mathematics at American schools, colleges, and universities. Learn more about me at
/ premath
Mathematical Olympiad | Algebra Problem | Math Olympiad Preparation
Olympiad Mathematical Question! | Learn Tips how to solve Olympiad Question without hassle and anxiety!
#OlympiadMathematics #OlympiadPreparation #CollegeEntranceExam
#PreMath #PreMath.com #MathOlympics #HowToThinkOutsideTheBox #ThinkOutsideTheBox #HowToThinkOutsideTheBox?
#OlympiadMathematicalQuestion #HowToSolveOlympiadQuestion #MathOlympiadQuestion #MathOlympiadQuestions #OlympiadQuestion #Olympiad #AlgebraReview #Algebra #Mathematics #Math #Maths
#MathOlympiadPreparation #LearntipstosolveOlympiadMathQuestionfast #OlympiadMathematicsCompetition #MathOlympics #SolveSystemofEquations
#blackpenredpen #SolveForX #RationalEquation #RationalEquations #SolveRationalEquation #SolveRationalEquations #SolveExponentialEquation #SolveExponentialEquations #ExponentialEquation #ExponentialEquations #SolveTheRationalEquation #SolveTheExponentialEquation #AlgebraProblem #MathematicalOlympiad #OlympiadMathematics
How to solve Olympiad Mathematical Question
How to prepare for Math Olympiad
How to Solve Olympiad Question
Solve for X
How to Solve international math olympiad questions
international math olympiad questions and solutions
international math olympiad questions and answers
olympiad mathematics competition
blackpenredpen
math olympics
olympiad exam
olympiad exam sample papers
math olympiad sample questions
math olympiada
British Math Olympiad
olympics math
olympics mathematics
olympics math activities
olympics math competition
Math Olympiad Training
How to win the International Math Olympiad | Po-Shen Loh and Lex Fridman
Po-Shen Loh and Lex Fridman
Number Theory
There is a ridiculously easy way to solve this Olympiad qualifier problem
This U.S. Olympiad Coach Has a Unique Approach to Math
The Map of Mathematics
mathcounts
math at work
exponential equation
system of equations
solve system of equations
solve the equation
pre math
Poh Shen Loh
Olympiad Mathematics
Subscribe Now as the ultimate shots of Math doses are on their way to fill your minds with the knowledge and wisdom once again.

[@wtspman]

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. 👍

[@PreMath]

Thank you for your Nice feedback! Cheers! You are awesome 😀

[@parmanandaggarwal546]

kzbin.info/www/bejne/epDYg2tthJuGgMU

[@ahmadnawazgohar9571]

let 3/7= u not (3/7);x =u

[@KayanHerdiana]

the first time when I saw this problem, I thought the value of x was 1 😂

[@DeepSmart]

U correct kayan

[@nyamjargalluvsannyam9750]

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!

[@parmanandaggarwal546]

kzbin.info/www/bejne/epDYg2tthJuGgMU

[@nickdyne8001]

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!

[@user-ly5bc4xd2s]

تمرين جميل رائع حقا . شكرا جزيلا لكم. والله يحفظكم ويرعاكم ويحميكم . تحياتنا لكم من غزة فلسطين .

[@mathsplus01]

Another elegant solution. Very encouraging. Thank you

[@theLordsboy]

Thanks for drawing my brain along into a nice orderly solution.

[@echandler]

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.

[@PreMath]

Great point! Thank you for your feedback! Cheers! You are awesome, Chandler 😀

[@parmanandaggarwal546]

kzbin.info/www/bejne/epDYg2tthJuGgMU

[@93307842]

I wonder, why math becomes so easy with your explanation. Waitung for others

[@JPTaquari]

Herr professor, here there is only one value for X, ONE Hugs from a Brazilian who loves math!

[@pietergeerkens6324]

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.

[@parmanandaggarwal546]

kzbin.info/www/bejne/epDYg2tthJuGgMU

[@anatoliy3323]

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!

[@parmanandaggarwal546]

kzbin.info/www/bejne/epDYg2tthJuGgMU

[@shlifejourney8151]

Like 341 Nice sharing sir. Your way of teaching is so easy to understand... thanks for sharing very helpful video...👍👍👍

[@parmanandaggarwal546]

kzbin.info/www/bejne/epDYg2tthJuGgMU

[@DrLiangMath]

Nice problem and good solution!

[@bobbravo9245]

Excellent explained 👍

[@sl2357]

Nice solution!

[@jkotsche7035]

master class!!!

[@denisallouche4576]

Bravo!

[@SuperYoonHo]

thanks😀

[@sonnyclief]

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

[@cos161]

Amazing

[@mariodistefano2973]

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?

[@SelebateNation]

12:00 have you heard of synthetic devision? it is very fast and easy

[@adrianmoscalu4429]

Nice ! Solution îs manipulation 3 and 7

[@Mark-cz2qe]

cool elegent answer

[@pinakiroy174]

A really simple problem presented so wittily. Perfect for JEE/ MBA entrance examinations. Brilliant.

[@PremSharma-bm3kq]

Much simple solution is possible

[@Shikuesi]

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.

[@rcnayak_58]

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.

[@FootballGalacticos]

I love your content. Any Biology and Agriculture problem can be channelled to The Eagle TV for assistance. Thank you❤

[@giuseppemalaguti435]

Divido N e D per 7^3x*3^3x....risulta dopo lunghi ma semplici calcoli x=1,-1

[@nicogehren6566]

great job

[@PreMath]

Glad to hear that! Thank you for your feedback! Cheers! You are awesome, Nico 😀

[@kalyanbasak6494]

🙏🏻 proffessor sir sharing reply x=1,-1

[@PreMath]

Excellent! Thank you for your feedback! Cheers! You are awesome, Kalyan 😀

[@thomaslange1624]

Beautiful

[@user-dv7bz9wt6o]

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.

[@nirupamasingh2948]

V nice

[@PreMath]

So nice of you. Thank you for your feedback! Cheers! You are awesome, Niru 😀

[@nirupamasingh2948]

@@PreMath Sir you go to the minutest detail with so much patience🙏🙏

[@hansschotterradler3772]

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.

[@PreMath]

Thank you for your feedback! Cheers! You are awesome, Hans 😀

[@parmanandaggarwal546]

kzbin.info/www/bejne/epDYg2tthJuGgMU

[@jimtwisted1984]

What happened to the 3 power 2 in the denominator?

[@HappyFamilyOnline]

Very nice step by step tutorial👍👍 😋 Thanks for sharing

[@parmanandaggarwal546]

kzbin.info/www/bejne/epDYg2tthJuGgMU

[@keithwood6459]

I notice there's not the usual huge crowd of people explaining how THEY did it! Just a few this time.

[@christianthomas9863]

At first glance, x=1 is a solution because 27+342 =370 and 63+147=210, so 370/210 équals the LHS.

[@jsjiang6120]

Solving the equation is easy. What I am wondering is who and how to invent this equation.

[@mardiahharun9379]

the answer is x-1, solve it using try and chec strategy.

[@Aaravsrivastava117]

i solve it successfully

[@djtmaga639]

Good problem to review and get your hands dirty with algebra.

[@PreMath]

Good point! Thank you for your feedback! Cheers! You are awesome, DJT 😀

[@susennath6035]

Nice explanation

[@PreMath]

Thanks for liking Cheers! You are awesome, Susen 😀

[@sarangmasal680]

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

[@devondevon4366]

x=1

[@murdock5537]

370/210 = 37/21

[@marshalls36]

好，奖 1 万元

[@aaravm1627]

E

[@hanasuajipi8702]

román to number

[@sachinnaidoo1559]

My eyes ouch ... use a black background please 🙏

[@harshitsharma1520]

actually the value of x is nothing in my life because I don't have any x

[@coolvideos5550]

5th comment

[@PreMath]

Thanks! Cheers! You are awesome 😀

[@Teamstudy4595]

Very Simple ans : x = 1

[@e1woqf]

-1 works as well

[@johnau8793]

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.

[@olgakornak3969]

_______ 37÷21=1.761904

[@Teamstudy4595]

4th comment

[@PreMath]

Thanks Jayant