Question

Solve the following equations.
$\sqrt{x+5}-\sqrt{x-3}=2$

Answer 1

We have, $\sqrt{x+5}-\sqrt{x-3}=2$

squaring both side we have

$(x+5)+(x-3)-2\times \sqrt{x+5}\times \sqrt{x-3}=4$

$2x+2-2\sqrt{(x+5)(x-3)}=4$

$2x-2=2\sqrt{(x+5)(x-3)}$

$x-1=\sqrt{(x+5)(x-3)}$

again squaring both side we have,

$(x-1{)}^2=(\sqrt{x+5\left)\right(x-3)}{)}^2$

$x^2+1-2x=(x+5)(x-3)$

$x^2+1-2x=x^2+2x-15$

$4x-16=0$

$4x=16$

$x=4$