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Question 30
if a+b+c=9 and ab+bc+ca=26, find a2+b2+c2.

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Solution

Given,
a+b+c=9 and ab+bc+ca=26 …..(i)
Now,
a + b + c = 9
On squaring both sides, we get,
(a+b+c)2=(9)2
a2+b2+c2+2ab+2bc+2ca=81
[Using the identity, (a+b+c)2=a2+b2+c2+2ab+2bc+2ca]
a2+b2+c2+2(ab+bc+ca)=81
a2+b2+c2+2(26)=81 [from eq.(i)]
a2+b2+c2=8152=29

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