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Question Number 164543 by cortano1 last updated on 18/Jan/22

$$\frac{4\sqrt{1-x}}{x}+\frac{\sqrt{2x-1}}{1-x}=3\sqrt{3}$$

Answered by leonhard77 last updated on 19/Jan/22

$$\left(1\right)1-x>0\cap 2x-1⩾0$$$$\frac{1}{2}⩽x<1$$$$\left(2\right)let\sqrt{x}=\cos t$$$$\frac{4\sin t}{\cos {}^{2}t}+\frac{\sqrt{\cos 2t}}{\sin {}^{2}t}=3\sqrt{3}$$$$4\sin {}^{3}t+\cos {}^{2}t\sqrt{\cos 2t}=\frac{3\sqrt{3}}{4}\sin {}^{2}2t$$$$$$

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