Question
If $a + b + c = 11$ and $a^2 + b^2 + c^2 = 81,$ find $: ab + bc + ca.$
✓
Answer
Since $(a+b+c)^2=a^2+b^2+c^2+2(a b+b c+c a)$
$\therefore(11)^2=81+2(a b+b c+c a)$
$\therefore 2(a b+b c+c a)=121-81=40$
$a b+b c+c a=\frac{40}{2}$
$\Rightarrow \mathrm{ab}+\mathrm{bc}+\mathrm{ca}=20$
$\therefore(11)^2=81+2(a b+b c+c a)$
$\therefore 2(a b+b c+c a)=121-81=40$
$a b+b c+c a=\frac{40}{2}$
$\Rightarrow \mathrm{ab}+\mathrm{bc}+\mathrm{ca}=20$
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