Question : If $(a + b + c) = 14$ and $(a^{3} + b^{3} + c^{3} - 3 a b c) = 98$ , find the value of $(a^{2} + b^{2} + c^{2})$ .
Option 1: 70
Option 2: 64
Option 3: 68
Option 4: 72

Question

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

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Answer 1

Correct Answer: 70

Solution : $a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - a c)$ .
Given that:
$(a + b + c) = 14$ and $(a^{3} + b^{3} + c^{3} - 3 a b c) = 98$
So, $98 = 14 (a^{2} + b^{2} + c^{2} - a b - b c - a c)$
⇒ $(a^{2} + b^{2} + c^{2}) = 7 + a b + b c + a c$ ...(i)
We know that, $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + a c)$ ...(ii)
From equation (i),
$(14)^{2} = 7 + 3 (a b + b c + a c)$
⇒ $(a b + b c + a c) = 63$
Substituting the above value in an equation (i),
$(a^{2} + b^{2} + c^{2}) = 7 + 63$
⇒ $a^{2} + b^{2} + c^{2} = 70$
So, the value of $(a^{2} + b^{2} + c^{2})$ is 70.
Hence, the correct answer is 70.

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Question : If (a+b+c)=14 and (a3+b3+c3−3abc)=98, find the value of (a2+b2+c2).Option 1: 70Option 2: 64Option 3: 68Option 4: 72

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Question : If $(a + b + c) = 14$ and $(a^{3} + b^{3} + c^{3} - 3 a b c) = 98$ , find the value of $(a^{2} + b^{2} + c^{2})$ .
Option 1: 70
Option 2: 64
Option 3: 68
Option 4: 72