Thread: I need help on this ratio problem.

Okay. Here is the problem.

2(x^2+ y^2) = 5xy

Please try to solve it.

Thank you.

Hello, necromancer745!

The instructions are missing.
We can't solve an equation with two variables in it.

I'll assume that we want the ratio: y/x

2(x² + y²) .= .5xy

We have: .2x² + 2y² .= .5xy . → . 2y² - 5xy + 2x² .= .0

Divide by x²: .2(y/x)² - 5(y/x) + 2 .= .0


Let u = y/x

and we have: .2u² - 5u + 2 .= .0

. . which factors: .(u - 2)(2u - 1) .= .0

. . and has roots: .u .= .2, ½


Back-substitute and we have: .y/x = 2 .and .y/x = ½