Carcass wrote:

If the average of m and \((x + y)^2 = x^2 + y^2\) , what is the value of m ?

A. x-y

B. x+y

C. (x-y)(x+y)

D. \((x-y)^2\)

E. \((x+y)^2\)

The average of m and (x + y)² = x² + y²So: [m + (x + y)²]/2 = x² + y²

Multiply both sides by 2 to get: m + (x + y)² = 2x² + 2y²

Expand left side to get: m + x² + 2xy + y² = 2x² + 2y²

Subtract x² from both sides to get: m + 2xy + y² = x² + 2y²

Subtract y² from both sides to get: m + 2xy = x² + y²

Subtract 2xy from both sides to get: m = x² - 2xy + y²

Factor right side to get: m = (x - y)²

Answer: D

Cheers,

Brent

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Brent Hanneson – Creator of greenlighttestprep.com

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