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If z^2+1/z^2=11 , find the value of z^3-1/z^3,using only the positive value of z-1/z
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If z^2+1/z^2=11 , find the value of z^3-1/z^3,using only the positive value of z-1/z

User Mike Stockdale
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1 Answer

5 votes
Hello,

Let's assume


t=z- (1)/(z) \\\\ t^2=z^2-2+ (1)/(z^2)= 11-2=9==\ \textgreater \ t=3\\\\ t^3=z^3-3z^2* (1)/(z) +3z* (1)/(z^2) - (1)/(z^3) \\\\ =z^3 - (1)/(z^3) -3(z-(1)/(z))\\\\ z^3 - (1)/(z^3)=t^3+3t=3^3+9=27+9=36
User Ankurvsoni
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