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Question Number 171043 by mathlove last updated on 06/Jun/22

$$A\in R$$$$A=\frac{\sqrt{x-2}+x+3}{\sqrt{4-2x}+x-1}faindA=?$$

Answered by MJS_new last updated on 07/Jun/22

$$\sqrt{x-2}\in \mathbb{R}\Rightarrow x⩾2$$$$\sqrt{4-2x}=\sqrt{2}\sqrt{2-x}\in \mathbb{R}\Rightarrow x⩽2$$$$\Rightarrow x=2$$$$\Rightarrow A=5$$

Commented by Rasheed.Sindhi last updated on 07/Jun/22

$$\mathbb{G}\mathbf{reat}\mathbf{sir}!$$

Commented by MJS_new last updated on 07/Jun/22

$$\mathrm{there}\mathrm{are}\mathrm{solutions}\mathrm{with}x\notin \mathbb{R}\wedge A\in \mathbb{R}$$$$\mathrm{simply}\mathrm{set}A\in \mathbb{R}\mathrm{and}\mathrm{solve}\mathrm{for}x\in \mathbb{C}$$$$A=5\Rightarrow x=2\vee x=-\frac{17}{16}\pm \frac{5\sqrt{2}}{8}\mathrm{i}$$

Commented by mathlove last updated on 08/Jun/22

$$thanks$$

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