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For what positive value of m will the following equation be true if n = 5?

\((m + n)^2 + (m - n)^2 + m^2 + n^2 = 318\)

 Aug 30, 2020
 #1
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The answer is m = 18.

 Aug 30, 2020
 #2
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Solve for m:
25 + (m - 5)^2 + m^2 + (m + 5)^2 = 318

Expand out terms of the left hand side:
3 m^2 + 75 = 318

Subtract 75 from both sides:
3 m^2 = 243

Divide both sides by 3:
m^2 = 81

Take the square root of both sides:

 m = 9                                     or     m = -9[discard]

 Aug 30, 2020

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