Question

Find the value of (z4 + 1/z4) if (z + 1/z) = 3

Answer 1

Explanation:

`z + (1)/(z)=3\\\\\\Square \ both \ sides\\\\(z+(1)/(z))^(2)=3^(2)\\\\\\z^(2)+(1)/(z^(2))+2*z*(1)/(z)=9\\\\\\z^(2)+(1)/(z^(2))+2=9\\\\\\z^(2)+(1)/(z^(2))=9-2\\\\\\z^(2)+(1)/(z^(2))=7\\\\\\Now, \ again \ square \ both \ sides,\\\\\\(z^(2)+(1)/(z^(2)))^(2)=7^(2)\\\\\\(z)^(4)+(1)/(z^(4))+2*z^(2)*(1)/(z^(2))=49\\\\\\z^(4)+(1)/(z^(4))+2=49\\\\\\z^(4)+(1)/(z^(4))=49-2\\\\z^(4)+(1)/(z^(4))=47`