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KVPY2016MathematicsQuadratic Equation

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

Options

  1. Athere is no solution pair (a, b)
  2. Bthere are infinitely many solution pairs (a, b)
  3. Cthere are exactly two solution pairs (a, b)
  4. Dthere is exactly one solution pair ( a , b )

Correct answer

D. there is exactly one solution pair ( a , b )

Step-by-step solution

array l (1+a+b)²=3 (1+a²+b² ) 1 a+a b+1 b=1²+a²+b² 1=a=b array exactly one pair.

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