Question

Sqrt(2−7x) -sqrt(x 3) =3

Answer 1

$(a+b)^2=a^2+2ab+b^2 \\ \\ \sqrt{2-7x} - \sqrt{x+3} =3 \\ (\sqrt{2-7x})^2 =(3 + \sqrt{x+3})^2\\2-7x=9+6\sqrt{x+3}+x+3 \\ 2-7x-9-x-3=6\sqrt{x+3} \\ (-8x-10)^2=(6\sqrt{x+3})^2 \\64x^2+160x+100=36(x+3) \\ 64x^2+160x+100=36x+108\\ 64x^2+160x-36x+100-108=0 \\ 64x^2+`124x-8=0 \\ 4( 16x^{2} +31x-2)=0$
$16x^{2} +31x-2=0 \\(x-2)(16x-1)=0 \\ x+2=0 \\ x=-2 \\ 16x-1=0 \\ x= \frac{1}{16}$

$\sqrt{2-7 \cdot\frac{1}{16} } - \sqrt{\frac{1}{16} +3} \neq 3 \\ x=-2$