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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

\dots \dots \dots \dots \dots \dots

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