ABC26GN1211 · Simplification

Subject: General Aptitude · Chapter: Simplification · Exam: · Marks: · Difficulty:

If $a+b+c=13, a^{2}+b^{2}+c^{2}=69$, then find $a b+b c+c a$.
(a)- 50
(b)50
(c)69
(d)75
Answer
Answer (as printed): B
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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