Question

If a minus b=5 and a square minus b square =65,then find the value of a square+b square

Answer 1

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Answer 2

$a - b = 5 = > a= 5 + b \\ {a}^{2} - {b}^{2} = 65 \\ (5 + b )^{2} - {b}^{2} =65 \\ 25 + 10 b + {b}^{2} - {b}^{2} = 65 \\ 25 + 10b = 65 \\ 10b = 40 \\ b = 4 \\ \\ a - b = 5 \\ a - 4 = 5 \\ a = 9$
$\\ \\ {a}^{2} + {b}^{2} = {9}^{2} + {4}^{2} \\ = 81 + 16 = 97$