Goal: to show y(adsbygoogle = window.adsbygoogle || []).push({}); ^{n}=x

This particular part of the proof supposes that y^{n}>x. So we want

an h>0 such that (y-h)^{n}>x

y^{n}-(y-h)^{n}<y^{n}-x

y^{n}-(y-h)^{n}=(y-(y-h))(y^{n-1}+y^{n-2}(y-h)+...+(y-h)^{n-1})<hny^{n-1}

this yields h=(y^{n}-x)/(ny^{n-1})

my question: how the heck does one derive h from this????

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# Homework Help: Very difficult algebra problem (real analysis)

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