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Math Help - If p+q=3 and pq=2, find 1/p^2 + 1/q^2.

  1. #1
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    Unhappy If p+q=3 and pq=2, find 1/p^2 + 1/q^2.

    Hi, i know this is probably a very simple problem to solve but i just cant figure it out.


    Question: if p+q=3 and pq=2, find the value of 1/p(squared) + 1/q(squared) without finding the values of p and q.



    If anyone could help me I would be very happy. Please let me know.


    Jessica
    Last edited by mr fantastic; October 23rd 2010 at 02:41 PM. Reason: Re-titled.
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Find:

    (p+q)^2 first.

    Then, it'll be easier.
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  3. #3
    Senior Member Sambit's Avatar
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     \frac{1}{p^2} + \frac{1}{q^2} = \frac{p^2 + q^2}{p^2q^2}
    now the numerator can be written as (p+q)^2 - 2pq and the denominator is  (pq)^2

    after this you should be able to do this by yourself.
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  4. #4
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    but isnt (p+q)2 : p(squared)+ 2pq + q(squared) ? :S
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  5. #5
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    Quote Originally Posted by Sambit View Post
     \frac{1}{p^2} + \frac{1}{q^2} = \frac{p^2 + q^2}{p^2q^2}
    now the numerator can be written as (p+q)^2 - 2pq and the denominator is  (pq)^2

    after this you should be able to do this by yourself.


    Thank you, helped alot.
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