Math Olympiad Algebra Problem Solving Tricks | Radical Equation Simplification | Find "x" ?

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In this Math Olympiad Algebra Problem, you'll learn tips and tricks of solving International Math Olympiad exams quickly. #IMO #matholympiad #algebra #radicalequations #simplify #exponential

[@mr.freire9167]

12:50 Instead of checking if m > 0 you checked if y > 0. As showed in the video, to find m you have to raise y to the 6th power and any number raised to an even power is positive, therefore in all 3 cases m > 0, so the 3 cases has real roots.

[@superacademy247]

I've realized I made some mistakes. I'll redo this video to correct the mistakes

[@elmer6123]

Substitute x=m^(1/6) into the given equation and rearrange to x^3+x^2-1/8=0. By inspection x=-1/2. Divide by (x+1/2): x^2+x/2-1/4=0 yields x=(-1±√5)/4=-Φ/2 or 1/(2Φ) where Φ=(1+√5)/2 is the Golden Ratio. m=z^6=(-1/2)^6=1/64; m=x^6=Φ^6/64=(8Φ+5)/64=(18+8√5)/128=(9+4√5)/64 m=x^6=1/(64Φ^6)=(5-8/Φ)/64=(10+8-8√5)/128=(9-4√5)/64

[@ichdu6710]

Just discovered this fact: if x^3+x^2-1/8=0, then a solution must be between x=0 and x=1. also for the original equation m must be m >=0

[@ashrafsafwat3688]

Wrong solution.for example, M raised to 1/6 if raised to the power 6 it will be converted to m and raising the other side to 6 too will result in a real solution regardless being positive or negative.

[@yuusufliibaan1380]

❤❤❤ nice 💯🙂💯 thanks dear teacher ☺️

[@superacademy247]

Always welcome

[@richardleveson6467]

What's especially ingenious is the arithmetic in the last part where you avoid having to raise to the sixth power!

[@richardleveson6467]

Clever solution! Most enjoyable.

[@justekiara1953]

We came from far to get there. Many thanks.

[@moemirza1865]

-1/2 is on of the answers. Replace and verify?

[@superacademy247]

I've noted some errors. I'll do a similar video today to show the way forward