Question 50582
(sqrt (x+7)) + (sqrt x) = 3

Square both sides to get:
(x+7)+2sqrt(x(x+7))+x = 9
2sqrt(x^2+7x)=-2(x-1)
sqrt(x^2+7x)=-(x-1)
Square both sides to get:
x^2+7x=x^2-2x+1
9x=1
x=1/9
Checking the answer:
sqrt((1/9)+(63/9)) + sqrt((1/9))=3
sqrt(64/9)+sqrt(1/9)=3
8/3 + 1/3 = 3
3=3

cheers,
Stan H.