Question

If a + b + c = 12 and $a^2+b^2+c^2=50$; find ab + bc + ca

• A. (x+2)
• B. (x + 2) (x + 3)
• C. (x+3)
• D. x(x+1)

Answer 1

The correct option is D

x(x+1)

Given that

$a+b+c=12;$
Squaring on both sides , we have
$(a+b+c{)}^2={12}^2$
$a^2+b^2+c^2+2(ab+bc+ca)=144$
Given $a^2+b^2+c^2=50$;
$50+2(ab+bc+ca)=144$
$2(ab+bc+ca)=94$
$(ab+bc+ca)=47$