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

$$2x+\sqrt{x}=\frac{1}{2}$$$$8x+\frac{1}{\sqrt{x}}=?$$

Answered by MJS_new last updated on 01/Jun/22

$$\sqrt{x}\in \mathbb{R}\Rightarrow x⩽0$$$$\mathrm{let}\sqrt{x}=t⩾0$$$$2t^2+t-\frac{1}{2}=0\Rightarrow t=\sqrt{x}=\frac{-1+\sqrt{5}}{4}\Rightarrow x=\frac{3-\sqrt{5}}{8}$$$$\Rightarrow$$$$8x+\frac{1}{\sqrt{x}}=4$$

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