SOLUTION: The sum of the squares of two numbers is 256 and the square of their sum is 784. What is the product of the two numbers?

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Question 894317: The sum of the squares of two numbers is 256 and the square of their sum is 784. What is the product of the two numbers?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Two numbers, x and y.
x%5E2%2By%5E2=256 and %28x%2By%29%5E2=784

The 784 equation is x%5E2%2By%5E2%2B2xy=784; subtract the circle 256 equation from it:
2xy=784-256
2xy=528
highlight_green%28xy=264%29----THE ACTUAL ANSWER TO THE QUESTION
y=264%2Fx, and try substituting this into the circle equation.

x%5E2%2B%28264%2Fx%29%5E2=256
x%5E4%2B264=256x%5E2
x%5E4-256x%5E2%2B264=0
Solve for x%5E2
Discriminant: 256%5E2-4%2A264=64480
which is 2%5E5%2A5%2A13%2A31
x%5E2=%28256%2B-+4sqrt%284030%29%29%2F2
highlight%28x=0%2B-+%28%28256%2B-+4sqrt%284030%29%29%2F2%29%29, which is four different values.

This is not really finished.
Still want to find y for each of those x values.

Note, the actual question was to find the product of x and y, which was actually found early in this work.
highlight%28xy=264%29.