x(3sin((√x))−2(√x))=sin^3 ((√x))


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Question Number 157227 by amin96 last updated on 21/Oct/21

$x (3 \sin (\sqrt{x}) - 2 \sqrt{x}) = \sin^{3} (\sqrt{x})$
	Answered by Javokhir last updated on 21/Oct/21

	$\sqrt{x} = t$ $t^{2} (3 s i n t - 2 t) = {s i n}^{3} t (t = 0 ✓)$ $t \neq 0$ $3 - \frac{2 t}{s i n t} = \frac{{s i n}^{2} t}{t^{2}} \Rightarrow \frac{s i n t}{t} = z$ $z^{2} = 3 - \frac{2}{z} \Rightarrow z^{3} - 3 z + 2 = 0 z^{3} - z - 2 (z - 1) = 0$ $(z^{2} - 2) (z - 1) = 0 \Leftrightarrow s i n t = t$ $s i n t = \sqrt{2} t s i n t = - \sqrt{2} t$ $. . . . . . . . . . . . . . . . . .$
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