Find the ratio of x to y: (2x^2 + y^2)/x = (12y-x)/4

Answer 1

Luke, this is an unusual problem, but it is solvable.

(2x^2 + y^2)/x = (12y-x)/4

cross multiply

4(2x^2 + y^2) = x(12y-x)

multiply out

8x^2 + 4y^2 = 12xy -x^2

collect terms

9x^2 -12xy + 4y^2 = 0

Solve for x using quadratic formula

X = (12y +- sqrt(144y^2-4*9*4y^2)) / 18

X= 12y / 18

X/y = 12/18 = 2/3

Check answer

Set x = 2; y = 3

(8 + 9)/2 = (36-2)/4

17/2 = 34/4

Sorry, don’t know how to show you how without doing it myself.

Answer 2

Find the ratio of x to y: (2x^2 + y^2)/x = (12y-x)/4

(2x^2 + y^2) / x = (12y - x) / 4

Divide out each side:

2x + y^2 / x = 3y - x/4

y^2 / x = 3y - 9x/4

Divide both sides by y:

y/x = 3 - 9x/4y = (12y - 9x)/4y

x/y = 4y/(12y - 9x)