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State whether the statement is true or false.

On adding $a 2 + 3 a b − b c, b 2 + 3 b c − c a$ and $c 2 + 3 c a − a b$ , we get $a 2 + b 2 + c 2 + 2 a b + 2 b c + 2 c a .$

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True

False

answer is A.

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Detailed Solution

Adding,

a 2 + 3 a b − b c, b 2 + 3 b c − c a

and

c 2 + 3 c a − a b

.
On combining the like terms and then on adding the expression, we get,

a 2 + 3 a b − b c + b 2 + 3 b c − c a + c 2 + 3 c a − a b = a 2 + 3 a b − b c + b 2 + 3 b c − c a + c 2 + 3 c a − a b = a 2 + b 2 + c 2 + 2 a b + 2 b c + 2 c a

Therefore, the given statement is true.
Hence, option 1 is correct.

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