Question

If $a^2+b^2+c^2=31$ and $ab+bc+ca=25$, then $a+b+c$ is equal to

• A. $81$
• B. $56$
• C. $9$
• D. $6$

Answer 1

The correct option is C $9$

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

Given that: $a^2+b^2+c^2=31$ and $ab+bc+ca=25$

Substituting the values in the above formula we get,

$(a+b+c{)}^2=a^2+b^2+c^2+2ab+2bc+2ca\Rightarrow (a+b+c{)}^2=a^2+b^2+c^2+2(ab+bc+ca)\Rightarrow (a+b+c{)}^2=31+(2\times 25)\Rightarrow (a+b+c{)}^2=31+50\Rightarrow (a+b+c{)}^2=81\Rightarrow a+b+c=\sqrt{81}\Rightarrow a+b+c=9$

Hence, $a+b+c=9$.