Question

Simplify the equation.
$\sqrt{x^2+ax+a^2}+\sqrt{x^2+ax-ab}=a+b$

Answer 1

$\sqrt{x^2+ax+a^2}+\sqrt{x^2+ax-ab}=(a+b)$

$\sqrt{x^2+ax+a^2}=(a+b)-\sqrt{x^2+ax-ab}$

Squaring both side

$x^2+ax+a^2={(a+b)}^2+\left(x^2+ax-ab\right)$ $-2(a+b)\sqrt{x^2+ax-ab}$

$2(a+b)\sqrt{x^2+ax-ab}=b^2+ab$

$2\sqrt{x^2+ax-ab}=b$

Squaring again

$4(x^2+ax-ab)=b^2$

Simplified equation $:4x^2+4ax-4ab-b^2=0$