Question
If $a^2 + b^2 + c^2 = 41$ and $a + b + c = 9;$ find $ab + bc + ca.$
✓
Answer
$(a + b + c)^2 = (9)^2$
$a^2 + b^2 + c^2 + 2ab + 2bc + 2ca = 81$
$\Rightarrow 41 + 2(ab + bc + ca) = 81$
$\Rightarrow 2(ab + bc + ca)$
$= 81 - 41$
$= 40$
$\Rightarrow ab + bc + ca$
$= 20.$
$a^2 + b^2 + c^2 + 2ab + 2bc + 2ca = 81$
$\Rightarrow 41 + 2(ab + bc + ca) = 81$
$\Rightarrow 2(ab + bc + ca)$
$= 81 - 41$
$= 40$
$\Rightarrow ab + bc + ca$
$= 20.$
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