Question : If $a^{2} + b^{2} + c^{2} = 14$ and $a + b + c = 6$ , then the value of $(a b + b c + c a)$ is:
Option 1: 11
Option 2: 12
Option 3: 13
Option 4: 14

Question

Question : If $a + b + c$ = 6 and $a b + b c + c a$ = 11, then the value of $b c (b + c) + c a (c + a) + a b (a + b) + 3 a b c$ is:

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Answer 1

Correct Answer: 11

Solution : Given: $a^{2} + b^{2} + c^{2} = 14$ and $a + b + c = 6$ .
On squaring the given equation $a + b + c = 6$ , we get,
$(a + b + c)^{2} = 6^{2}$
⇒ $a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a) = 36$
Substitute the value of $a^{2} + b^{2} + c^{2} = 14$ in the above equation and we get,
⇒ $14 + 2 (a b + b c + c a) = 36$
⇒ $2 (a b + b c + c a) = 22$
⇒ $(a b + b c + c a) = 11$
Hence, the correct answer is 11.

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Question : If a2+b2+c2=14 and a+b+c=6, then the value of (ab+bc+ca) is:Option 1: 11Option 2: 12Option 3: 13Option 4: 14

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Question : If $a^{2} + b^{2} + c^{2} = 14$ and $a + b + c = 6$ , then the value of $(a b + b c + c a)$ is:
Option 1: 11
Option 2: 12
Option 3: 13
Option 4: 14