SOLUTION: the sum of the squares of two numbers is 65 and the squares of their sum is 121. find the numbers. Thanks in advance.

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Question 1072669: the sum of the squares of two numbers is 65 and the squares
of their sum is 121. find the numbers. Thanks in advance.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
I changed the numbers.  But the steps are the same.  

system%28x%5E2%2By%5E2=45%2C%28x%2By%29%5E2=81%29

%28x%2By%29%5E2=81%29

x%5E2%2B2xy%2By%5E2=81%29

x%5E2%2By%5E2%2B2xy=81%29

%28x%5E2%2By%5E2%29%2B2xy=81%29

Substitute 45 from the other equation for x2+y2:

45%2B2xy=81%29

2xy=36

xy=18

y=18%2Fx

Substitute in 

x%5E2%2By%5E2=45

x%5E2%2B%2818%2Fx%29%5E2=45

x%5E2%2B324%2Fx%5E2=45

x%5E4%2B324=45x%5E2

x%5E4-45x%5E2%2B324=0

%28x%5E2-9%29%28x%5E2-36%29=0

%28x-3%29%28x%2B3%29%28x-6%29%28x%2B6%29=0

x-3=0; x+3=0;  x-6=0;  x+6=0
  x=3;   x=-3;   x=6;   x=-6

Use this as a model to do yours.

Edwin