If \( \Large a+b+c=14\ and\ a^{2}+b^{2}+c^{2}=96 \), then \( \Large \left(ab+bc+ca\right)=? \)


A) 51

B) 55

C) 50

D) 65

Correct Answer:
C) 50

Description for Correct answer:
We know that,

\( \Large \left(a+b+c\right)^{2}= \left(a^{2}+b^{2}+c^{2}\right)+2 \left(ab+bc+ca\right) \)

=>\( \Large 196=96+2 \left(ab+bc+ca\right) \)

=>\( \Large 2 \left(ab+bc+ca\right)=196-96=100 \)

Therefore, \( \Large \left(ab+bc+ca\right)=\frac{100}{2}=50 \)

Part of solved Simplification questions and answers : >> Elementary Mathematics >> Simplification








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