If: a + b + c = 14 and a^2 + b^2 + c^2 = 96, then (ab + bc + ca) is

The correct answer is Option (2) → 50

We use the identity:

$(a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab+bc+ca)$

Given:

$a+b+c = 14 \Rightarrow (a+b+c)^2 = 196$

$a^2+b^2+c^2 = 96$

Substitute:

$196 = 96 + 2(ab+bc+ca)$

$2(ab+bc+ca) = 100$

$ab+bc+ca = 50$