If: $a + b + c = 14$ and $a^2 + b^2 + c^2 = 96$, then $(ab + bc + ca)$ is |
96 50 14 82 |
50 |
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: $196 = 96 + 2(ab+bc+ca)$ $2(ab+bc+ca) = 100$ $ab+bc+ca = 50$ |