Answered

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

Find The Real And Imaginary Solution Of W3 10000 class=

Sagot :

Explanation

Given

[tex]w^3-1000=0[/tex]

We will have;

[tex]\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)}\frac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\frac{-1+\sqrt{3}i}{2} \\ therefore;\text{ }w=\sqrt[3]{1000},\:w=\sqrt[3]{1000}\frac{-1+\sqrt{3}i}{2},\:w=\sqrt[3]{1000}\frac{-1-\sqrt{3}i}{2} \\ hence;w=10,w=10\times\frac{-1+\sqrt{3}i}{2},\:w=10\times\frac{-1-\sqrt{3}i}{2} \\ w=10,\:w=-5+5\sqrt{3}i,\:w=-5-5\sqrt{3}i \end{gathered}[/tex]

Answer: Option D

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