SOLUTION: if x+y=10 and xy=21 then evaluate x^3+y^3

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Question 989741: if x+y=10 and xy=21 then evaluate x^3+y^3
Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
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You have the system of two equations

system+%28x%2By+=+10%2C%0D%0Axy=21%29.

Express  y  from the first equation   y = 10-x   and substitute it into the second equation.  You will have

x*(10-x) = 21,

x%5E2+-+10x+%2B+21 = 0.

Apply the quadratic formula to solve this quadratic equation. You will get

x%5B1%5D = 3,   x%5B2%5D = 7.

It means that the original system has the solutions

x = 3,  y = 7       and
x = 7,  y = 3.

Based on it,  calculate   x%5E3 + y%5E3.