Câu hỏi của Iien Pham

Question

Tìm x ϵ N và x>2

x(x-1) . x(x-1) = (x-2)xx(x-1)

Ngô Đức Phong · Accepted Answer

$x.\left(x-1\right).x.\left(x-1\right)=\left(x-2\right).x.x.\left(x-1\right)\left(x\in N;x>2\right)$

$\Rightarrow\left(x^2-x\right).\left(x^2-x\right)=\left(x-2\right).x^2.\left(x-1\right)$

$\Rightarrow x^4-x^3-x^3+x^2=\left(x-2\right).\left(x-1\right).x^2$

$\Rightarrow x^4-2x^3+x^2=\left(x^2-x-2x+2\right).x^2$

$\Rightarrow x^4-2x^3+x^2=x^4-x^3-2x^3+2x^2$

$\Rightarrow x^4-2x^3+x^2-x^4+x^3+2x^3+2x^2=0$

$\Rightarrow x^4-x^4+2x^3-2x^3+2x^2+x^2+x^3=0$

$\Rightarrow x^2.\left(2+1+x\right)=0$

$\Rightarrow x^2=0hoac2+1+x=0$

$\Rightarrow x^2=0^2$ $\Rightarrow3+x=0$

$\Rightarrow x=0;\Rightarrow x=-3$

Mà $x\in N;x>2$

$\Rightarrow x\in\varnothing$

Vậy $x\in\varnothing$

Chúc bn học tốtCâu trả lời: $x.\left(x-1\right).x.\left(x-1\right)=\left(x-2\right).x.x.\left(x-1\right)\left(x\in N;x>2\right)$