If $(a - b) = 7$ and $a b = 9$ then $(a^{2} + b^{2}) = ?$
(a) 67
(b) 31
(c) 40
(d) 58

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Solution

$a - b = 7, a b = 9 a^{2} + b^{2} = (a - b)^{2} + 2 a b = (7)^{2} + 2 \times 9 = 49 + 18 = 67$

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