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Find : a2+b2...

Question

Find : $a^{2} + b^{2} + c^{2}$ , if $a + b + c = 9$ and $a b + b c + c a = 24$

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Solution

Formula ${(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)$
Substituting $a + b + c = 9; a b + b c + c a = 24$
$9^{2} = a^{2} + b^{2} + c^{2} + 2 (24)$
$81 - 48 = a^{2} + b^{2} + c^{2}$
$a^{2} + b^{2} + c^{2} = 33$

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