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    Find a condition on p such that y=x^2+px/x^2+p takes all values as x varies

    I just dont get it I know that x^2+p cannot equal 0 but then have no clue what to do.
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    (Original post by Econowizard)
    Find a condition on p such that y=x^2+px/x^2+p takes all values as x varies

    I just dont get it I know that x^2+p cannot equal 0 but then have no clue what to do.
    If x^2+p > 0 then what does that imply about p?
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    (Original post by Desmos)
    If x^2+p > 0 then what does that imply about p?
    p greater than minus square root x.... but that isnt the answer
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    (Original post by Econowizard)
    Find a condition on p such that y=x^2+px/x^2+p takes all values as x varies
    I guess this is y=\dfrac{x^2+px}{x^2+p}?

    If you choose any k \in \mathbb{R}, you want to be able to find an x \in \mathbb{R} such that k=\dfrac{x^2+px}{x^2+p} has a solution. But that is equivalent to saying that

    k(x^2+p)=x^2+px

    has a real solution (i.e. a real choice of x) for any choice of k. Can you carry on?
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    (Original post by Econowizard)
    p greater than minus square root x.... but that isnt the answer
    no no nooooooooooooooooooooooooooooooo ooooooooooooooooooo

    first is can x²+p ever equal 0?

    if so find the value of x which does so

    if not then what is the minimal value of x²+p
 
 
 
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