SOLUTION: Find one pair of real numbers, (x,y), such that x + y = 6 and x^3 + y^3 = 144.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find one pair of real numbers, (x,y), such that x + y = 6 and x^3 + y^3 = 144.       Log On


   

Question 1075730: Find one pair of real numbers, (x,y), such that x + y = 6 and x^3 + y^3 = 144.
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.
x%5E3+%2B+y%5E3 = 144

is equivalent to

%28x%2By%29%2A%28x%5E2+-+xy+%2B+y%5E2%29 = 144.

Replace here (x+y) by 6 (due to the first equation) and cancel both sides by the factor of 6. You will get 

x%5E2+-+xy+%2B+y%5E2 = 24.

Now, from the first equation express x = 6-y and substitute it into the last equation. You will get

%286-y%29%5E2+-%286-y%29%2Ay+%2B+y%5E2 = 24.


Simplify and solve this quadratic equation.