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Question

If a+b+c=9 and ab+bc+ca=26, then the value of a2+b2+c2−3 is _______.

A
25
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B
29
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C
28
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D
26
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Solution

The correct option is D 26
Given:
a+b+c=9ab+bc+ca=26

Squaring on both sides of a+b+c=9, we get
(a+b+c)2=81

We know that, (a+b+c)2=a2+b2+c2+2(ab+bc+ca)]
81=a2+b2+c2+2(ab+bc+ca)
Substituting the value of ab+bc+ca=26 in the above expression,
81=a2+b2+c2+2(26)
=8152=a2+b2+c2=29

a2+b2+c23=293=26

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