Question

if [z-1/z]=6, find [z+1/z]

Answer 1

Answer:

$2 \sqrt{10}$

Step-by-step explanation:

given:-

$z - \frac{1}{z } = 6 \\ \\ squaring \: both \: side \: \\ {(z - \frac{1}{z} })^{2} = {(6)}^{2} \\ \\ {z }^{2} + \frac{1}{ {z}^{2} } - 2 = 36 \\ \\ {z}^{2} + \frac{1}{ {z}^{2} } = 38$

Now

${z}^{2} + \frac{1}{ {z}^{2} } = {(z + \frac{1}{z} })^{2} - 2 \\ \\ 38 = ({z + \frac{1}{z} })^{2} - 2 \\ \\ z + \frac{1}{z} = \sqrt{40} \\ \\ z + \frac{1}{z} = 2 \sqrt{10}$