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Question

If a+b+c=11 and a2+b2+c2=81, then find ab+bc+ca.

A
121
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B
40
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C
30
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D
20
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Solution

The correct option is D 20

Formula (a+b+c)2=a2+b2+c2+2(ab+bc+ca)
Substituting a+b+c=11;a2+b2+c2=81
112=81+2(ab+bc+ca)
12181=2(ab+bc+ca)
ab+bc+ca=402=20


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