SOLUTION: Given x^3 + x^2 * y - 20 = 0 and y^3 + x * y^2 - 45 = 0 what is y? It is also given that x and y are positive real numbers

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Question 1119601: Given x^3 + x^2 * y - 20 = 0 and y^3 + x * y^2 - 45 = 0 what is y?
It is also given that x and y are positive real numbers
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This approach was not yet rechecked carefully.....
First Equation,
x%5E3%2Bx%5E2y=20
x%5E2%28x%2By%29=20
x%2By=20%2Fx%5E2

Second Equation,
xy%5E2%2By%5E3=45
y%5E2%28x%2By%29=45
x%2By=45%2Fy%5E2

Two expressions for x+y are equal.
20%2Fx%5E2=45%2Fy%5E2
y%5E2%2Fx%5E2=9%2F4
y%2Fx=0%2B-+3%2F2


Assuming the PLUS form would work,
x=2y%2F3
Substitute this into the second equation:
y%5E3%2B%282%2F3%29y%2Ay%5E2-45=0
y%5E3%2B%282%2F3%29y%5E3=45
%285%2F3%29y%5E3=45
y%5E3=45%2A%283%2F5%29
y%5E3=%289%2A5%2A3%29%2F5=9%2A3=3%5E3
highlight_green%28y=3%29

Solution not yet been checked carefully