Solve (2)y=1-sqrt[3]{(x-2)^2}

$$( 2 ) y = 1 - \sqrt[ 3 ] { ( x - 2 ) ^ { 2 } }$$

Solve for y

$$y=\frac{-\left(x-2\right)^{\frac{2}{3}}+1}{2}$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.

$$2y=1-\sqrt[3]{x^{2}-4x+4}$$

The equation is in standard form.

$$2y=-\sqrt[3]{x^{2}-4x+4}+1$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{-\left(x-2\right)^{\frac{2}{3}}+1}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{-\left(x-2\right)^{\frac{2}{3}}+1}{2}$$

Solve for x (complex solution)

$$x=\left(1-2y\right)^{3}+2$$

$$y=\frac{1}{2}\text{ or }arg(1-2y)<\frac{2\pi }{3}$$

Solve for x

$$x=-\left(1-2y\right)^{\frac{3}{2}}+2$$

$$x=\left(1-2y\right)^{\frac{3}{2}}+2\text{, }y\leq \frac{1}{2}$$