Suppose m and n are positive integers. If (m + n) 2 = 49 and mn = 10, then what is the value of m 2 + n 2?

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If (m + n) 2 = 49 and mn = 10

sqrt (m + n) 2 = m+n and sqrt 49 = 7

m + n = 7

m = 7 - n

Substituting ....n(7-n) = 10

7n - n^2 = 10

n^2 - 7n + 10 = 0

n = 2

m = 5

So m^2 + n^2 = 5^2 + 2 ^2 = 25 + 4 = 29

= 29

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