Find : a^2 + b^2 + c^2, if a + b + c = 9 and ab + bc + ca = 24 - Vidyadip

Question

Find : $a^2 + b^2 + c^2,$ if $a + b + c = 9$ and $ab + bc + ca = 24$

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Answer

$a+ b + c = 9$
$\Rightarrow (a + b + c)^2 = (9)2$
$\Rightarrow a^2 + b^2+ c^2 + 2ab + 2bc + 2ca = 81$
$\Rightarrow a^2+ b^2 + c^2+ 2(ab + bc + ca) = 81$
$\Rightarrow a^2 + b^2 + c^2+ 2\times 24 = 81$
$\Rightarrow a^2 + b^2+ c^2 + 48 = 81$
$\Rightarrow a^2 + b^2+ c^2= 81 − 48$
$\Rightarrow a^2 + b^2 + c^2 = 33$

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