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      Question

      If x4 + 2x3 + ax2 + bx

      + 9 is a perfect square, where a and b are positive real numbers, then the value of a and b are
      A a = 5, b = 6 Correct Answer Incorrect Answer
      B a = 6, b = 7 Correct Answer Incorrect Answer
      C a = 7, b = 6 Correct Answer Incorrect Answer
      D a = 7, b = 8 Correct Answer Incorrect Answer

      Solution

      X4 + 2x3 + ax2 + bx + 9 is perfect Square. ⇒ we know that (a+b+c)2 = a²+b²+C²+2ab+2bc+2ca ⇒ if we take a = x², b = x, c = 3 and put all three values in formula's we get ⇒ (x2+x+3)2 = x4+x²+9+2x3+6x +6x2 ⇒ x4 +7x2 +2x3 +9 +6x ----- (2) Compare eq (2) with Given eq we get ⇒ a = 7 and b = 6

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