Question : If $(a + b + c) = 16$ and $(a^{2} + b^{2} + c^{2}) = 90$ , find the value of $(a b + b c + c a)$ .
Option 1: 84
Option 2: 83
Option 3: 82
Option 4: 81

Question

Question : If $(a + b + c) = 14$ and $(a^{3} + b^{3} + c^{3} - 3 a b c) = 98$ , find the value of $(a^{2} + b^{2} + c^{2})$ .

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Answer 1

Correct Answer: 83

Solution : We have, $(a + b + c) = 16$ and $a^{2} + b^{2} + c^{2} = 90$
We know that $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)$
So, $16^{2} = 90 + 2 (a b + b c + c a)$
⇒ $a b + b c + c a = \frac{16^{2} - 90}{2} = 83$
Hence, the correct answer is 83.

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Question : If (a+b+c)=16 and (a2+b2+c2)=90, find the value of (ab+bc+ca).Option 1: 84Option 2: 83Option 3: 82Option 4: 81

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Question : If $(a + b + c) = 16$ and $(a^{2} + b^{2} + c^{2}) = 90$ , find the value of $(a b + b c + c a)$ .
Option 1: 84
Option 2: 83
Option 3: 82
Option 4: 81