Question

(x-5)^4=(x-5)^6

Answer 1

\(\Leftrightarrow\left(x-5\right)^4\cdot\left[\left(x-5\right)^2-1\right]=0\)

=>(x-5)(x-4)(x-6)=0

=>\(x\in\left\{4;5;6\right\}\)

Answer 2

`@` `\text {Ans}`

`\downarrow`

`(x-5)^4 = (x-5)^6`

`=> (x-5)^4 - (x-5)^6 = 0`

`=> (x-5)^4 - (x-5)^2 (x-5)^4 = 0`

`=> (x-5)^4 * [ 1 - (x-5)^2] = 0`

`=> (x-5)^4 * [ (x-4)(x-6)] = 0`

`=> (x-5)(x-4)(x-6) = 0`

`=>`\(\left[{}\begin{matrix}x-5=0\\x-4=0\\x-6=0\end{matrix}\right.\)

`=>`\(\left[{}\begin{matrix}x=5\\x=4\\x=6\end{matrix}\right.\)

Vậy, `x \in {5; 4; 6}.`