Question

If $a+b+c=12$ and $a^2+b^2+c^2=50$, then ab + bc + ca = .

• A. $88$
• B. $47$
• C. $84$
• D. $94$

Answer 1

The correct option is B $47$

It is given that $a+b+c=12$

Using identity ,
$(a+b+c{)}^2=a^2+b^2+c^2+2(ab+ac+bc)$, we have

${12}^2=a^2+b^2+c^2+2(ab+ac+bc)$

Substituting the value of $a^2+b^2+c^2$ which is 50,we get
$144=50+2(ab+ac+bc)$
$⟹$$2(ab+ac+bc)=144-50$
$⟹$$2(ab+ac+bc)=94$
$⟹ab+ac+bc=47$