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

1 answer:

7 0

Hello,

Let's assume

$t=z- \dfrac{1}{z} \\\\

t^2=z^2-2+ \dfrac{1}{z^2}= 11-2=9==\ \textgreater \ t=3\\\\

t^3=z^3-3z^2* \dfrac{1}{z} +3z* \dfrac{1}{z^2} - \dfrac{1}{z^3} \\\\
=z^3 - \dfrac{1}{z^3} -3(z-\dfrac{1}{z})\\\\
z^3 - \dfrac{1}{z^3}=t^3+3t=3^3+9=27+9=36


$

You might be interested in

Which equation represents the graph?

klio [65]

The second option.

That is because
$y -3 = - \frac{1}{2}(x + 1) \\ (y -3)+3 = (- \frac{1}{2} x - \frac{1}{2}) + 3 \\ y = - \frac{1}{2}x + 2 \frac{1}{2}$