If a + b + c = 9 and ab + bc + ca = 26, find a^2 + b^2 + c^2. - Vidyadip

Question

If $a + b + c = 9$ and $ab + bc + ca = 26$, find $a^2 + b^2 + c^2.$

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Answer

We have that $(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + bc + 2ca$
$\Rightarrow (a + b + c)^2 = (a^2 + b^2 + c^2) + 2(ab + bc + ca)$
$\Rightarrow 9^2 = (a^2 + b^2 + c^2) + 2(26)$ [Putting the value of $a + b + c$ and $ab + bc + ca]$
$\Rightarrow 81 = (a^2 + b^2 + c^2) + 52$
$\Rightarrow (a^2 + b^2 + c^2) = 81 - 52 = 29$

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