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VIT Engineering VIT Engineering Solved Paper-2011

  • question_answer
    If one AM A and two GM p and q are inserted between two given numbers, then find the value of \[\frac{{{p}^{2}}}{q}+\frac{{{q}^{2}}}{p}.\]

    A)  A

    B)  2A

    C)  3A

    D)  4A

    Correct Answer: B

    Solution :

    Let a and b are two numbers. Then, \[A=\frac{a+b}{2}\] ?(i) Also, a, p, q, b are in GP. \[\therefore \] \[\frac{p}{a}=\frac{q}{p}=\frac{b}{q}\] \[\Rightarrow \] \[\frac{{{p}^{2}}}{q}=a\] and \[\frac{{{q}^{2}}}{p}=b\] \[\therefore \]  \[\frac{{{p}^{2}}}{q}+\frac{{{q}^{2}}}{p}=a+b=2A\] [using Eq. (i)]


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