by **Luke53** on Fri Apr 15, 2011 10:55 am

OK thanks, I can see where I went wrong.

Squaring both sides of the first eqn. sqrt(x) + sqrt(y) = 25 gives: x + y + 2 *(sqrt(x) *sqrt(y)) = 625

The second eqn. gives me: x + y = 533

So: 2 * (sqrt(x) *sqrt(y)) = 625 - 533 and so: sqrt(x) * sqrt(y) = 46

Squaring this on both sides gives: x * y = 2116

Out of the system: x * y = 2116 and x + y = 533 I get the quadratic eqn.: -(y^2) + 533 y - 2116 = 0 ; solving it yields: y = 4 or y = 529 ; (this is what I'm looking for).

I've got the same result doing it the way you suggested me:

Out of enq. (2): x = 533 - y and putting this in eqn. (1), yields: sqrt(533 - y) + sqrt(y) = 25

Sqaring both sides gives: 533 - y + 2*(sqrt(533 - y) * sqrt(y)) + y = 625 the y's cancelling out)

2 * qsrt(533 - y) * sqrt(y) = 92 so sqrt(533 -y) * sqrt(y) = 46

Squaring both sides of the last eqn. gives me : (533 - y) * y = 2116 => -(y^2) + 533y - 2116 = 0

I knew the results of that eqn.

Great stuff!