1, \(x^3-x-3=2\sqrt{6x-x^2}\)
2, \(x^3+6x^2-171x-40\left(x+1\right)\sqrt{5x-1}+20=0\)
3, \(\sqrt[3]{x+3}+\sqrt[3]{x-3}=\sqrt[5]{x-5}+\sqrt[5]{x+5}\)
4. \(\left(\frac{1}{\sqrt{x}}-\frac{\sqrt{x}}{x+1}\right)^2=\frac{4\left(1+\sqrt{1+4x}\right)}{x+1+\sqrt{x^2+3x+2}}\)