Question

If $\left(a+b+c\right)=15$ and $\left(ac+bc+ca\right)=74$, find the value of $\left(a^2+b^2+c^2\right)$

Answer 1

$(a+b+c)=15;ab+bc+ca=74$

To find $(a^2+b^2+c^2)$
$(a+b+c{)}^2=(a^2+b^2+c^2)+2(ab+bc+ca)$

$(15{)}^2=(a^2+b^2+c^2)+2(74)$

$225=(a^2+b^2+c^2)+148$

$(a^2+b^2+c^2=77$

$\therefore a^2+b^2+c^2=77$