I have the irrational equation ##\sqrt{x - 1} + \sqrt{2 - x} = 0##, which has no real solutions. However, when I try to solve the equation, I get a real solution, that is:(adsbygoogle = window.adsbygoogle || []).push({});

##\sqrt{x - 1} + \sqrt{2 - x} = 0##

##\sqrt{x - 1} = -\sqrt{2 - x}##

##(\sqrt{x - 1})^{2} = (-\sqrt{2 - x})^{2}##

##(\sqrt{x - 1})(\sqrt{x - 1}) = (-\sqrt{2 - x})(-\sqrt{2 - x})##

##x - 1 = 2 - x##

##x = \frac{3}{2}##

What am I doing wrong here? In which step am I making a mistake?

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# Solving an irrational equation

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