49.8k views
3 votes
Find the real and imaginary solution of (w^3) - 1000=0

Find the real and imaginary solution of (w^3) - 1000=0-example-1

1 Answer

7 votes

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

User Pyano
by
9.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories