Question

Find the real and imaginary solution of (w^3) - 1000=0

Answer 1

Step-by-step explanation

Given

`w^3-1000=0`

We will have;

`\begin{gathered} w^3=1000 \\ \mathrm{For\:}x^3=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}(-1-√(3)i)/(2),\:\sqrt[3]{f\left(a\right)}(-1+√(3)i)/(2) \\ therefore;\text{ }w=\sqrt[3]{1000},\:w=\sqrt[3]{1000}(-1+√(3)i)/(2),\:w=\sqrt[3]{1000}(-1-√(3)i)/(2) \\ hence;w=10,w=10*(-1+√(3)i)/(2),\:w=10*(-1-√(3)i)/(2) \\ w=10,\:w=-5+5√(3)i,\:w=-5-5√(3)i \end{gathered}`

Answer: Option D