MathematicsIf x= p+2q + p−2q p+2q − p−2q  . Then, which of the following is the value of  q x 2 −px+q  ?

If x= p+2q + p2q p+2q p2q  . Then, which of the following is the value of  q x 2 px+q  ?


  1. A
    0
  2. B
    1
  3. C
    2
  4. D
    None of these 

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    Solution:

    Consider the given question,
    p+2q + p2q p+2q p2q   Rationalizing the denominator,
    We get,  x= p+2q + p2q p+2q p2q × p+2q + p2q p+2q + p2q    x= ( p+2q + p2q ) 2 ( p+2q ) 2 ( p2q ) 2   x= ( p+2q + p2q ) 2 (p+2q)(p2q)   We know that,
    (a+b) 2 = a 2 + b 2 +2ab  
    Simplifying the equation (i),
    x= p+2q+p2q+2( p+2q )( p2q ) p+2qp+2q    x= 2p+2 p 2 4 q 2 4q    x= p+ p 2 4 q 2 2q   2xqp= p 2 4 q 2 (ii)  
    Squaring both sides of the equation (ii),
    Hence, the value of q x 2 px+q=0   .
    Therefore, option 1 is correct.
     
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