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The question says: "Find the minimum value of $px+qy$ when $xy=r^2$."

No information is given on $p,q,x,\text{and }y.$ However assuming the obvious I tried using this, but I am not able reduce it to the desired answer, which is $2pq\sqrt{3}$.

Any ideas?

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    @MaX: Then practicing on the real questions is the way to go. Exam questions tend not to change fundamentally from year to year. You will need to solve too many of these questions in too little time, so you need to develop a deep familiarity with possible questions.2011-11-30

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By am-gm, we have

$px+qy \geq 2 \sqrt{pqxy} =2r \sqrt{pq}$

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    @Zarrax, that would make it rather redundant I think.2011-11-30
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Blindly assuming all the variables are greater than $0$ (otherwise you can send it to $-\infty$) you can write $px+qy=px+qr^2/x$. Differentiating and setting to zero gives $x=qr/p$ and plugging in gives $px+qy=2r\sqrt{pq}$. Is your $\sqrt{3}$ supposed to be $r$?