2x-x-1-2-8x-1-x-

Question Number 170849 by mathlove last updated on 01/Jun/22

2 x + \sqrt{x} = \frac{1}{2}

8 x + \frac{1}{\sqrt{x}} = ?

Answered by MJS_new last updated on 01/Jun/22

\sqrt{x} \in R \Rightarrow x ⩽ 0

let \sqrt{x} = t ⩾ 0

2 t^{2} + t - \frac{1}{2} = 0 \Rightarrow t = \sqrt{x} = \frac{- 1 + \sqrt{5}}{4} \Rightarrow x = \frac{3 - \sqrt{5}}{8}

\Rightarrow

8 x + \frac{1}{\sqrt{x}} = 4

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