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Question

Consider the equation (1+a+b)2=3(1+a2+b2), where a,b are real numbers. Then

A
there is no solution pair (a,b)
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B
there are infinitely many solution pairs (a,b)
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C
there are exactly two solution pairs (a,b)
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D
there is exactly one solution pair (a,b)
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Solution

The correct option is D there is exactly one solution pair (a,b)
(1+a+b)2=3(1+a2+b2)1+a2+b2+2ab+2a+2b=3+3a2+3b2a22ab+b2+a22a+1+b22b+1=0(ab)2+(a1)2+(b1)2=0Since, all square terms will be non-negative.Hence, all must be zero.a=b=1,Hence, only one possible pair of solution.

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