Question

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

• A. $26$
• B. $27$
• C. $28$
• D. $29$

Answer 1

The correct option is D $29$

Given, $a+b+c=9$ and $ab+bc+ca=26$.

We know, $(a+b+c{)}^2=a^2+b^2+c^2+2ab+2bc+2ca$

$\Rightarrow (a+b+c{)}^2=a^2+b^2+c^2+2(ab+bc+ca)$.

Putting the values here, we get,

$(9{)}^2=a^2+b^2+c^2+2(26)$

$\Rightarrow 81=a^2+b^2+c^2+52$

$\Rightarrow a^2+b^2+c^2=81-52=29$.

Hence, option $D$ is correct.