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NDA2015MathematicsQuadratic EquationActual

If 2 p+3 q=18 and 4 p^2+4 p q-3 q^2-36=0 , then what is (2 p+q) equal to?

Options

  1. A6
  2. B7
  3. C10
  4. D20

Correct answer

C. 10

Step-by-step solution

aligned & 4 p^2+4 p q-3 q^2-36=0 & (4 p^2+4 p q+q^2 )-4 q^2-36=0 & (2 p+q)^2=4 q^2+36 & 2 p+3 q=18 & p= 18-3 q 2 & [ 18-3 q 2 2+q ]^2=4 q^2+36 & (18-3 q+q)^2 & (18-2 q)^2=4 q^2+36 & 324+4 q^2-72 q=4 q^2+36 & 72 q=324-36=288 aligned q = 288 72 =4 Putting the value of q in 2 p+3 q=18 aligned & 2 p+3 4=18 & 2 p=18-12 & p= 6 2 =3 & (2 p+q)=2 3+4=10 aligned Option (C) is correct.

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