Question

Find the real or imaginary solutions solutions of the following equation by factoring. y^3-512=0Choose the correct answer below.

Answer 1

B

1) The best way to tackle this question is to think of the difference between two cubes:

`x^3-y^3=(x-y)(x^2+xy+y^2)`

2) So now, let's apply to the binomial we have:

`\begin{gathered} \sqrt[3]{512}=8 \\ y^3-512=(y-8)(y^2+8y+64) \end{gathered}`

So now, let's make use of the factor zero property for the first factor and solve the quadratic using the quadratic formula:

`\begin{gathered} y-8=0,y=8 \\ \\ y_=(-8\pm√(8^2-4\cdot\:1\cdot\:64))/(2) \\ y_1=(-8+8√(3)i)/(2)=\quad4+4√(3)i \\ y_2=(-8-8√(3)i)/(2)=\quad-4-4√(3)i \end{gathered}`

3) Thus, the answer is:

B