Question

Solve the following equation:
$2\sqrt{x-1}+\sqrt{x+3}=2$

Answer 1

Squaring on both sides

$4(x-1)+(x+3)+4\sqrt{(x^2+2x-3)}=4$

$⟹4\sqrt{(x^2+2x-3)}=5(1-x)$

squaring on both sides

$⟹16(x-1)(x+3)=25(1-x)(1-x)$

$⟹16x+48=25x-25$

$⟹x=1,8.11$ (approx)