Math Olympiad | A Nice Algebra Problem | A Nice Radical Equation

[@MathsOnlineVideos]

Nice problem. I will give it to my learners.

[@SALogics]

All the best ❤

[@prasad4844]

As always it was a pleasure to watch.thank you 🙏

[@SALogics]

Glad you enjoyed it! ❤

[@raghvendrasingh1289]

(x^2-2)^2 = 2-x subtracting x^2 both sides and factorising LHS (x^2-2 +x) (x^2-2-x) = 2-x-x^2 transposing RHS term to LHS and taking common (x^2+x-2) (x^2-x-1) = 0 (x+2) (x-1) ( x2-x-1) = 0 and so on

[@SALogics]

Very nice trick! ❤

[@souzasilva5471]

What would it look like if you exchanged 2 for 5?

[@SALogics]

It would be nice! ❤

[@ChavoMysterio]

√[2-√(2-x)]=x Domain: 1≤x≤2 2-√(2-x)=x² x²-2=-√(2-x) x⁴-4x²+4=2-x x⁴-4x²+x+2=0 x²(x²-4)+x+2=0 x²(x+2)(x-2)+1(x+2)=0 (x+2)[x²(x-2)+1]=0 (x+2)(x³-2x²+1)=0 (x+2)(x³-x²-x²+1)=0 (x+2)[x²(x-1)-(x²-1)]=0 (x+2)[x²(x-1)-(x-1)(x+1)]=0 (x+2)(x-1)(x²-x-1)=0 x+2=0 x=-2 see domain x²-x-1=0 4x²-4x-4=0 4x²-4x+1=5 (2x-1)²=5 |2x-1|=√5 2x-1=-√5 2x=1-√5 x=½(1-√5) see domain 2x-1=√5 2x=1+√5 x=½(1+√5) ❤ x-1=0 x=1 ❤

[@SALogics]

Very nice trick! I really appreciate that ❤

[@cabasantbab]

X=1

[@SALogics]

Very nice! ❤

[@prollysine]

by faktoring , (x-1)(x^3+x^2-3x-2)=0 , x=1 , x^3+x^2-3x-2=0 , (x+2)(x^2-x-1)=0 , x= -2 , x^2-x-1=0 , x=(1+/-V(1+4))/2 , x= (1+V5)/2 , (1-V5)/2 , x= 1 , -2 , (1+V5)/2 , (1-V5)/2 , test , -2 , (1+V5)/2 , (1-V5)/2 not a solu , solu , x= 1 ,

[@SALogics]

Very nice! ❤

[@borisjeud8464]

X=1

[@SALogics]

@@borisjeud8464 You guessed right! ❤

[@gaiatetuya92]

最後解が見えない

[@SALogics]

終了画面のビデオのせいでしょうか？❤

[@gaiatetuya92]

@@SALogics そうです。すべての動画で最後ぎりぎりにならないように、また解答を最後にまとめて頂ければ幸いです。

[@SALogics]

@@gaiatetuya92 ああ、最終的な答えは x = 1 であることを理解しています。他の解決策は拒否されます。 x = -2、x = (1 + √5)/2、および x = (1 - √5)/2