- #1
Mr Davis 97
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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:
##\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?
##\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?