Math Olympiad Question | Can You Solve This?

Hello My Dear Family😍😍😍

I hope you all are well 🤗🤗🤗
If you like this video about
How to solve this algebra equations
Math Olympiad
please Like & Subscribe my channel ，🙏🙏🙏🙏
video #trending #viralvideo #viral
#maths #algebra #matholympiad #mathematics #math #exponentialequation

Some important playlist
💭Math Olympiad Questions

Hello Everyone 🤗🤗🤗

If you like this video about
Math Olympiad and
Nice Exponential Problem - How to Solve It
please Like & Subscribe my channel ，🙏🙏🙏🙏

#matholympiad
learncommunolizer Math Olympiad Question | college level |solving Exponential Equation
@mathwindow
@PreMath
@JusticeShepard
@bprpPrecalculus
@SyberMath
Topics Covered :-

international math Olympiad
Math Olympiad Problem
Algebra Problem
Olympiad Mathematics
System of Equations
math olympiad algebra problem
math
olympiad mathematics
math olympiad preparation
mathematics
maths
math olympiad questions
math olympics
math problems
olympiad
premath
math olympiad problems
challenging math problems
algebra
sybermath
algebra 1
algebra 2
sat math
quadratic equations
algebraic equations
nice algebra problem
olympiad exam 2022
pre math
imo
math olympiad question
high school math
math olympiad
how to study math
college math
algebra problem
precalculus
math olympiad problems with solutions
challenging math questions
trending math problem
olympiad trending math questions
difficult math equations
mathematical olympiad
challenging math
trending mathematics
olympiad math
algebra for beginners
math problems with solutions
math olympiad solutions
math competition solutions
solve for x
difficult math problems

#maths #algebra #mathematics #mathematician #mathematicians #algebra #algebratricks #algebraformulas #algebrahelp #olimpiadas #olimpiadmath #algebraquestion #algebraquestions #geometry #easymaths #easymathematics #easymathematicsforyou #multiplication #division #fraction #product #laws #lawsofexponent #howtolearnmathsfromthebeginning #howtolearnmathsfrombasics #howtolearnmaths #simplemathstricks #simplemathematics #simplemath #algebrahelp #simplealgebra#relaxingmath#howtosolvepotentialequations#potentialequations#solveforx#mathssolving#exponents #equations #exponentialequation #exponentialequations #algebrahelp #algebraformulas #algebratrick #highermathematics #highermaths #highermath#programming #programmer#sinus#sinx#cosx#findthevalueof #powerdivision#ln#derivative

[batavuskoga]

This explanation is difficult for an easy solution.
x²-1=(x-1)²
x²-1=x²-2x+1
-1=-2x+1
-1-1=2x
-2=-2x --> x=1
This is a much easier explanation than described in your video with the same result

[pieterhuman]

Foil the right hand side, cancei and solve. No need to look for complications where there aren't any.

[sifdlwe]

If you can't figure it out with just numbers and letters, it's a good idea to draw the curves of the expressions on the XY plane. y=(x-1)² is the parabola of y=x² shifted 1 parallel to the right, and touches the point where y=0, that is, the x-axis at (1, 0). y=x²-1 is the y=x² parabola shifted down by 1 and crosses the x-axis at (-1, 0), (1, 0). Therefore, the solution of (x-1)²=0 is only "1", and the solution of x²-1=0 is "-1 and 1". Since y=(x-1)² and y=x²-1 cross at (1, 0) and are parabolas of the same shape, they do not cross anywhere else. The solution of x²-1=(x-1)² is the point of cross of x, so it is one of "1". It's confusing because (1, 0) is the point of cross of the two curves and also the point of contact of y=(x-1)² with the x-axis.
In addition, y=x+1, which appears in the factorization, is the straight line y=x shifted up 1 parallel, and y=x-1 is shifted down 1 parallel, so (x+1)-(x-1 )=2, and x disappears and becomes a constant. Because the two lines are parallel, they never cross and there is no solution. y=x-1 crosses the x-axis at (1, 0), and it is also clear that the solution for x-1=0 is 1.

[timwood]

The lesson in this problem - as noted below - is to recognize when you might be dividing by zero, and not to go that way. But a lesson not taught by the video. Hmmm.

[SanePerson]

Square the rhs, subtract x² from both sides, and solve for x. Done. 
If you're concerned that in this process you missed another solution, just note that each side is a convex parabola, and they are similar, so they intersect only once, at x = 1.

[FractAlkemist]

All that algebraic manipulation is cool, but I'm an engineer not a theoretician.
My Python Genetic Algorithm gave me x = 1 in less than 5 seconds.
Cheers.

[edkjyxy]

Everything is Olympiad Math. The first person to solve this equation was also awarded a Fields Medal.

[amazingcalvin]

The weird thing about this particular problem is that it doesn't work when done in a particular way. We have x^2 - 1 = (x-1)^2. We can write this as (x-1)*(x+1) = (x-1)*(x-1). Cancelling x-1 from both sides, we get x+1 = x-1 leading to a paradox of 1 = -1. Since x=1 in this problem, I do vaguely get the idea that cancelling x-1 (which will be 0 in this problem) is not mathematically sound. But if I proceed from the first method alone, I still don't yet know that x=1 and so cancelling x-1 might seem like a good idea till I run into the equation that 1 = -1. It's only then I solved using another method. But this ultimately turns mathematics into a trial and error stuff which is what mathematics should not be. What am I doing wrong here? Why does expanding the (x-1)^2 and then solving for x give a valid solution of x=1 while doing this from the first method leads nowhere?

[John-niyt]

What if (x^2 -- 1) = (x -- 1)^24, would you solve the equation the same way?

[attilakiss]

I think this is too complicated, trying to find these tricks.
Much more natural to see that x^2 is the same on both sides, so if you put x^2-2x+1 then get a linear equation and a quick solution. And it needs much less elaboration (what is zero, when is zero etc.).

[michaelkovalenko]

I was taught how to solve that in 6th grade or so, using a much simpler approach:
factorize (x-1)(x+1) = (x-1)(x-1)
For x =1, this becomes 0 = 0, hence it's the solution
For x != 1, divide both sides by (x-1), which yields x+1=x-1, which is false for any x.

Therefore x=1 is the only solution

[gspaulsson]

This is the 0=0 fallacy. Plug 1 into the given equation and you get (1^2-1) = (1-1)=0 on the left and 1^2-2*1+1^2 = 1-2+1 = 0 on the right. You can use this trick to prove that 1=2 or 99=-99 or anything you like. Simple factorization: (x+1)(x-1)=(x-1)(x-1). x-1 on both sides cancel, leaving x+1=x-1, which is clearly impossible.

[jacekplacek]

5 second but film took 3:27 :) This is funny way to learning math from these films, good idea. In Poland nobody has so much time. :)

[stefancalin]

this is the worst way to solve a simple equation I have seen in a very long time ... x^2-1=x^2-2x+1 => x^2-1-x^2+2x-1=0 =>2x-2=0 => x=1 ... this is simply basic, any kid that has ever seen an equation can solve it, in max 15 seconds not 3 minutes of back and forth formulas that are simply unneeded

[SubhashishChakraborty]

Was this question asked in the Maths Olympiad for the chimpanzee’s?