Question

Solve the following equation:
$\sqrt{2x-4}-\sqrt{x+5}=1$

Answer 1

$\sqrt{2x-4}-\sqrt{x+5}=1$

$\Rightarrow (2x-4)+(x+5)-2\sqrt{x+5}\sqrt{2x-4}=1$

$\Rightarrow 3x+1-1=2\sqrt{x+5}\sqrt{2x-4}$

$\Rightarrow {\left(3x\right)}^2=4(x+5)(2x-4)$

$9x^2=4(2x^2+10x-4x-20)$

$9x^2=8x^2+24x-80$

$x^2-24x+80=0$

$x^2-20x-4x+80=0$

$x(x-20)-4(x-20)=0$

$(x-4)(x-20)=0$

$\Rightarrow x=4,20.$

Hence, the aanswer is $4,20.$