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

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

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Answer 1 · 2018-07-17T19:03:04

$x \approx 90.090492759$ $xapprox 90.090492759$

Explanation:

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

after squaring again and combinig like Terms we get

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

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

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

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