Question

If ($ab+bc+ca)$ = 26 and $a^2+b^2+c^2$ = 29,
then ($a+b+c$) is :

• A. 12
• B. 9
• C. 18
• D. 24

Answer 1

The correct option is B 9

Given, ($ab+bc+ca$) = 26 and $a^2+b^2+c^2$ = 29.
Using the identity $(a+b+c{)}^2$ = $a^2+b^2+c^2+2ab+2bc+2ca$,
$\Rightarrow$ $(a+b+c{)}^2$ = 29 + 2$\times$26
$\Rightarrow$ $(a+b+c{)}^2$ = 81
$\Rightarrow$ ($a+b+c$) = $\sqrt{81}$ = 9.