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Question

Evaluate If a + b + c = 15 and a2+b2+c2 = 125 , find ab + bc + ca


A

81

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B

50

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C

100

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D

75

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Solution

The correct option is B

50


We use the identity (a+b+c)2 = a2+b2+c2+2ab+2bc+2ca

Given a + b + c = 15 and a2+b2+c2 = 125

Hence (15)2 = 125+2(ab+bc+ca)

225=125+2(ab+bc+ca)

225125=2(ab+bc+ca)

100=2(ab+bc+ca)

Hence ab+bc+ca = 50


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