How do I evaluate $sqrt(x+10)=1/sqrt(x)+10$ to find its real solution(s)?

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Answer 1 · 2018-07-17T19:03:04

$xapprox 90.090492759$

We have $x>0$ and we can sqauare the equation:
$x-1/x-90=20/sqrt(x)$

after squaring again and combinig like Terms we get

$x^4-180x^3+8098x^2-220x+1=0$
by a numerical method we get $xapprox 90,09492749$

How do I evaluate sqrt(x+10)=1/sqrt(x)+10sqrt(x+10)=1/sqrt(x)+10 to find its real solution(s)?