inf{ z = x + x^(-1): x>0 } any help would be greatly appreciated!
Last edited by pseudonym; Nov 6th 2009 at 02:02 PM.
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Originally Posted by pseudonym in{ z = x + x^(-1): x>0 } any help would be greatly appreciated! What percisely are you having difficulties with?
Originally Posted by pseudonym in{ z = x + x^(-1): x>0 } For every $\displaystyle a~\&~b$ it follows that $\displaystyle a^2+b^2\ge 2ab.$. Equality holds only if $\displaystyle a=b$ For your problem let $\displaystyle a=\sqrt{x}~\&~b=\frac{1}{\sqrt{x}}.$
Originally Posted by Drexel28 What percisely are you having difficulties with? my understanding is that I have to find the greatest lower bound, i.e. the smallest value of x for z to exist?
Originally Posted by pseudonym my understanding is that I have to find the greatest lower bound, i.e. the smallest value of x for z to exist? Do you understand that every $\displaystyle z$ in your set is such that $\displaystyle z\ge 2?$
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