Question

if z^2+1/z^2=11 th3n find the value of z^3+1/z^3​

Answer 1

Answer:

$8\sqrt{13}$

Step-by-step explanation:

$z^2 + \frac{1}{z^2} = 11\\\\\Rightarrow z^2 + \frac{1}{z^2} + 2 = 13\\\\\Rightarrow (z + \frac{1}{z})^2 = 13$

$\Rightarrow z + \frac{1}{z} = \sqrt{13}\\\\\Rightarrow (z + \frac{1}{z})^3 = (13)^\frac{3}{2}\\\\\Rightarrow z^3 + \frac{1}{z^3} + 3 * z* \frac{1}{z} * (z + \frac{1}{z}) = (13)^\frac{3}{2}$

$\Rightarrow z^3 + \frac{1}{z^3} + 3 * \sqrt{13} = \sqrt{13 * 13 * 13}\\\\\Rightarrow z^3 + \frac{1}{z^3} = 13\sqrt{13} - 3\sqrt{13} = 8\sqrt{13}$

So there you go.