Given x^3 + x^2 * y - 20 = 0 and y^3 + x * y^2 - 45 = 0 what is y?

Question

It is given that x and y are positive real numbers.

 

Answer 1

Re-write the equations this way:

x²(x+y) = 20 and

y²(x+y) = 45

 

If x+y ≠ 0 and neither x nor y is 0, then

20/x² = 45/y² (because they are both equal to x + y)

 

y² = 9x²/4 => x =±3x/2

 

Substitute in the first equation:

x³ ± 3x³/2 = 20

 

The minus sign doesn't work in this problem...gives a negative answer

5x³/2 = 20 => x³ = 40/5 = 8

 

x = 2 and y = 3x/2 = 3

 

Substitute these answers into the original equations to make sure they are correct.