SOLUTION: the sum of the squares of two numbers is 72. The product of the two numbers is 36. Find the two numbers.

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Question 1103636: the sum of the squares of two numbers is 72. The product of the two numbers is 36. Find the two numbers.
Found 2 solutions by jorel1380, ikleyn:
Answer by jorel1380(3719)   (Show Source): You can put this solution on YOUR website!
Let m and n be your two numbers. Then:
m²+n²=72 and
mn=36
Therefore, n=36/m, so:
m²+(36/m)²=72
m^4+1296=72m²
m^4-72m²+1296=0
Solve for m and n
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Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
.
x^2 + y^2 = 72,    (1)
xy        = 36.    (2)

====================>

x^2 - 2xy + y^2 = 72 - 2*36 = 0  ====>


(x-y)^2 = 0  ====>  x = y  ====>


Then from (2)  x*x = 36   ====>  x^2 = 36  ====>  x = +/- 6.


The solutions are  (x,y) = (6,6)   and/or   (x,y) = (-6,-6).


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