Question

1/x^2 + 1/y^2=61/900, xy =30, solve for x, given x is positive only

Answer 1

Answer:

x+y=30

y=30−x

x(30−x)=144

30x−x2=144

−x2+30x−144=0

Use the quadratic formula:

x=−30±302−4(−1)(−144)√2(−1)

x=−30±900−576√−2

x=−30±324√−2

x=−30±18−2

x=24 or x=6

Which one satisfies the equations and the condition x>y?

If x=24, y=6. This satisfies both equations and the condition x>y

If x=6, y=24. This satisfies both equations, but it does not satisfy the condition x>y

That leaves us with one solution: x=24 and y=6

x−y=24−6=18