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Question Number 37733 by kunal1234523 last updated on 17/Jun/18

$$\mathrm{Prove}\mathrm{that}\mathrm{the}\mathrm{equation}\sin \theta =x+\frac{1}{x}$$$$\mathrm{is}\mathrm{impossible}\mathrm{if}x\mathrm{be}\mathrm{real}.$$

Answered by MrW3 last updated on 17/Jun/18

$$ifx>0:$$$$\sin \theta =x+\frac{1}{x}={(\sqrt{x}-\frac{1}{\sqrt{x}})}^2+2⩾2$$$$but\sin \theta ⩽1\Rightarrow nosolution$$$$$$$$ifx<0:$$$$\sin \theta =x+\frac{1}{x}=-{(\sqrt{-x}-\frac{1}{\sqrt{-x}})}^2-2⩽-2$$$$but\sin \theta ⩾-1\Rightarrow nosolution$$

Commented by kunal1234523 last updated on 17/Jun/18

$$\mathrm{thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{MrW}3$$

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