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Question Number 59270 by pete last updated on 07/May/19

$$\mathrm{Solve}\mathrm{the}\mathrm{equation}{3\mathrm{x}}^{\frac{1}{2}}+5-{2\mathrm{x}}^{\frac{1}{2}}=0$$

Answered by Joel578 last updated on 07/May/19

$$3\sqrt{x}+5-2\sqrt{x}=0$$$$\iff \sqrt{x}=-5$$$$\mathrm{But}\mathrm{for}x\in \mathbb{R},\sqrt{x}\mathrm{must}⩾0,\mathrm{so}\mathrm{the}\mathrm{equation}\mathrm{has}\mathrm{no}\mathrm{real}\mathrm{solution}$$

Commented by Joel578 last updated on 07/May/19

$$\mathrm{If}x=25i^4,\mathrm{then}\sqrt{x}=5i^2=-5$$$$\mathrm{Hence}\mathrm{the}\mathrm{equation}\mathrm{has}\mathrm{complex}\mathrm{solution}$$$$\mathrm{Am}\mathrm{I}\mathrm{wrong}?$$

Commented by pete last updated on 07/May/19

$$\mathrm{you}\mathrm{are}\mathrm{right}$$

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