If a+b+c=13, a²+b²+c²=69, then find a b+b c+c a. · ABC26GN1211
Subject: General Aptitude · Chapter: Simplification
If $a+b+c=13, a^{2}+b^{2}+c^{2}=69$, then find $a b+b c+c a$.
Answer
Explanation
$$\begin{aligned} (a+b+c)^{2}=a^{2}+b^{2} & +c^{2}+2(a b+b c+c a) \\ \Rightarrow \quad 2(a b+b c+c a) & =(a+b+c)^{2}-\left(a^{2}+b^{2}+c^{2}\right) \\ & =169-69=100 \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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