Question

Tìm x thuộc số tự nhiên biết: 

a) x³=x²

b) (x-1)⁴=(x-1)³

Answer 1

\(x^3=x^2\Rightarrow x\in\left\{0;1;-1\right\}\)

Vì: \(x\ge0\Rightarrow x\in\left\{0;1\right\}\)

Vậy: \(x\in\left\{0;1\right\}\)

\(\left(x-1\right)^4=\left(x-1\right)^3\Rightarrow\left(x-1\right)\in\left\{-1;0;1\right\}\)

\(x-1=-1\Rightarrow x=0\) (nhận)\(x-1=0\Rightarrow x=1\)(nhận)\(x-1=1\Rightarrow x=2\)(nhận)

Vậy: \(x\in\left\{0;1;2\right\}\)

Answer 2

a) \(x^3=x^2\)

\(\Rightarrow x^3:x^2=1\)

\(\Rightarrow x=1\)

Vậy \(x=1\)

b) \(\left(x-1\right)^4=\left(x-1\right)^3\)

\(\Rightarrow\left(x-1\right)^4:\left(x-1\right)^3=1\)

\(\Rightarrow x-1=1\)

\(\Rightarrow x=2\)

Vậy \(x=2\)