### Brain Teasers

# Sum of Squares

If the difference between two numbers is 9 and their product is 14, what is the sum of their squares?

### Answer

109You could solve this by setting up two equations:

X - Y = 9

X * Y = 14

and solving for X and Y (which equal approximately 10.35 and 1.35 or -1.35 and -10.35, respectively). Then take X^2 + Y^2 to get 109.

Or you could recognize that:

(X-Y)^2 = X^2 - 2*X*Y + Y^2

rearranging,

X^2 + Y^2 = (X-Y)^2 + 2*X*Y

The left side of this equation is what we're looking for. From the original two equations, we know that:

X-Y = 9 and therefore (X-Y)^2 = 81.

X*Y = 14 and therefore 2*X*Y = 28.

81 + 28 = 109, which is the answer.

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