If $a + b = 9, a b = 4$ , find the value of $a^{2} + b^{2}$ .

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Solution

a + b = 9 __ (1)
Squaring both sides
$(a + b)^{2} = 87$
$a^{2} + 2 a b + b^{2} = 87$
ab = 4 (2)
$a^{2} + 8 + b^{2} = 87$
$a^{2} + b^{2} = 73$

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