Question

Solve the following equation:
$\sqrt{2x+5}=8-\sqrt{x-1}$

Answer 1

$\sqrt{2x+5}=8-\sqrt{x-1}$

$\Rightarrow \sqrt{2x+5}+\sqrt{x-1}=8$

squaring both sides

$\Rightarrow 2x+5+x-1+2\sqrt{2x+5}\sqrt{x-1}=64$

$\Rightarrow 3x+4+2\sqrt{2x+5}x-1=64$

$\Rightarrow 2\sqrt{2x+5}\sqrt{x-1}=64-4-3x=60-3x=3(20-x)$

$\Rightarrow 4(2x+5)(x-1)=9(400+x^2-40x)$

$\Rightarrow 4(2x^2+5x-5-2x)=3600+9x^2-360x$

$\Rightarrow 8x^2+12x-20=3600+9x^2-360x$

$\Rightarrow x^2-372x+3620=0$

$\Rightarrow x=\frac{372\pm \sqrt{{372}^2-4\times 3620}}{2}$

$=\frac{372\pm \sqrt{123904}}{2}$

$\Rightarrow x=\frac{372\pm 352}{2}$

$\Rightarrow x=\frac{372+352}{2}=362$

and $x=\frac{372-352}{2}=\frac{20}{2}=10.$

Hence, solve.