Irrational Equations: Problems with Solutions

By Denitsa Dimitrova (Bulgaria)
Problem 1
$\sqrt{4+2x-x^2}=x-2$
Problem 2
$\sqrt{x^2-5}=\sqrt{x+1}$
Problem 3
$\sqrt{3x+10}-\sqrt{x+4}=2$
Problem 4
$\sqrt{x+2} - \sqrt{2x-3}=1$
Problem 5
$\sqrt{x-3}+\sqrt{2x+1}=\sqrt{3x+4}$
Problem 6
$\sqrt{2x+17}-1=x$
Problem 7
$\sqrt{x+3}-\sqrt{2-x}=1$
Problem 8
$\sqrt{1+4x-x^2}=x-1$
Problem 9
$\sqrt{1+x} + \sqrt{1-x}=1$
Problem 10
$x+\sqrt{\frac{x}{2}+2}=2$

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