Solve y=(x-3)^3+3

$$y = ( x - 3 ) ^ { 3 } + 3$$

Solve for y

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

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-3\right)^{3}.

$$y=x^{3}-9x^{2}+27x-27+3$$

Add -27 and 3 to get -24.

$$y=x^{3}-9x^{2}+27x-24$$

Solve for x (complex solution)

$$x=\sqrt[3]{y-3}+3$$

$$x=e^{\frac{4\pi i}{3}}\sqrt[3]{y-3}+3$$

$$x=e^{\frac{2\pi i}{3}}\sqrt[3]{y-3}+3$$

Solve for x

$$x=\sqrt[3]{y-3}+3$$