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Question Number 157805 by Huy last updated on 28/Oct/21

$$\mathrm{Find}\mathrm{x}\in \mathbb{R}:$$$${\mathrm{x}}^3-2\mathrm{x}+3=\sqrt{2\mathrm{x}+5}+4\sqrt{\mathrm{x}-1}$$

Answered by MJS_new last updated on 28/Oct/21

$$\mathrm{rhs}\mathrm{defined}\mathrm{for}x⩾1\mathrm{and}\mathrm{strictly}\mathrm{increasing}$$$$\mathrm{lhs}\mathrm{strictly}\mathrm{increasing}\mathrm{for}x>\frac{\sqrt{6}}{3}$$$$\Rightarrow \mathrm{only}1\mathrm{solution}⩾1$$$$\Rightarrow x=2(\mathrm{obvious}\mathrm{solution}8-4+3=\sqrt{9}+4\sqrt{1}=7)$$

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