Question

Solve:
$(x^2-2x+1{)}^{x^2-1}=1$.

Answer 1

$(x^2-2x+1{)}^{x^2-1}=1$

Possible values :- $x^2-1=0$

$\therefore x^2=1$

$\therefore x=\pm 1$

Also possible :- $x^2-2x+1=1$

$\therefore x^2-2x=0$

$\therefore x(x-2)=0$

$\therefore x=0$ OR $x=2$

Also possible :- $x^2-2x+1=-1$

$\therefore x^2-2x+2=0$

$\therefore (x-1{)}^2+1=0$

Not possible

$\therefore$ possible values :- $1,-1,0,2$