Question

If $a+b+c=9$ and $ab+bc+ca=26,$ then the value of $a^2+b^2+c^2$, is

• A. $29$
• B. $22$
• C. $16$
• D. $25$

Answer 1

The correct option is A $29$

Given, $a+b+c=9$ and $ab+bc+ca=26$
We know that,
${(a+b+c)}^2=a^2+b^2+c^2+2ab+2bc+2ac$
$\Rightarrow 9^2=a^2+b^2+c^2+2(ab+bc+ca)$
$\Rightarrow 81=a^2+b^2+c^2+2\left(26\right)$
$\Rightarrow a^2+b^2+c^2=81-52$
$\Rightarrow a^2+b^2+c^2=29$