if-2x-1-x-1-2-find-the-value-8x-1-x-

Question Number 181707 by amin96 last updated on 28/Nov/22

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

f i n d t h e v a l u e 8 x + \frac{1}{\sqrt{x}} = ?

Answered by mr W last updated on 29/Nov/22

t = \sqrt{x} > 0

f (t) = 2 t^{2} + \frac{1}{t}

\frac{d f}{d t} = 4 t - \frac{1}{t^{2}} = 0 \Rightarrow t = \frac{1}{\sqrt[3]{4}}

f_{m i n} = \frac{1}{\sqrt[3]{2}} + \sqrt[3]{4} \approx 2.381 > \frac{1}{2}

\Rightarrow 2 x + \frac{1}{\sqrt{x}} = \frac{1}{2} i s n o t p o s s i b l e f o r x \in R .

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