Question

Solve the following equation:
$\sqrt{x^2-2x+1}+\sqrt{x^2+2x+1}=2$

Answer 1

$\sqrt{x^2+2x+1}+\sqrt{x^2-2x+1}=2$

$\Rightarrow \sqrt{x^2+2x+1}=\sqrt{{(x+1)}^2}=x+1$

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

$\therefore \sqrt{x^2+2x+1}+\sqrt{x^2-2x+1}=2$

$\Rightarrow x+1+x-1=2$

$\Rightarrow 2x=2$

$\Rightarrow x=1$

Hence, the answer is $1.$