Question

Sqrt(2−7x) -sqrt(x 3) =3

Answer 1

`(a+b)^2=a^2+2ab+b^2 \\ \\ √(2-7x) - √(x+3) =3 \\ (√(2-7x))^2 =(3 + √(x+3))^2\\2-7x=9+6√(x+3)+x+3 \\ 2-7x-9-x-3=6√(x+3) \\ (-8x-10)^2=(6√(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= (1)/(16)`


`\sqrt{2-7 \cdot(1)/(16) } - \sqrt{(1)/(16) +3} \\eq 3 \\ x=-2`