Question

If z^2 1/z^2= 34 find the value of z^3 1/z^3 , using only the positive value of z 1/z

Answer 1

Hello,

Let's assume

$u=z+ \dfrac{1}{z} \\ u^2=(z+ \dfrac{1}{z} )^2=z^2+2*z* \dfrac{1}{z} + \dfrac{1}{z^2} =34+2=36\\ ==\ \textgreater \ \ u=6\\ (z+ \dfrac{1}{z} )^3=(z+ \dfrac{1}{z} )(z^2+z* \frac{1}{z} + \frac{1}{z^2} )\\ =6*(34+1)=210$