Correct Answer: Option B

Explanation

m² + n² = 29 .......(1)
m + n = 7 ............(2)

From (2),
m = 7 - n
but m² + n² = 29, substituting;
(7-n)² + n² = 29
49 - 14n + n² + n² = 29
=> 2n² -14n + 20 = 0
Thus n² -7n + 10 = 0

Factorizing;
(n-5)(n-2) = 0
n - 5 = 0, => n = 5
n - 2 = 0, => n = 2.

When n = 5,
m + n = 7, => m = 2,

When n = 2,
m + n = 7, => m = 5.

Thus (m,n) = (5,2) and (2,5)

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