Question

If( z-¹/z )=6, find the value of ( z²+¹/z²)​

Answer 1

Solution:

=> ( z - 1/z ) = 6

Squaring on both sides

=> ( z - 1/z )² = 6²

Using identify (a-b)² = a² + b² - 2ab

=> z² + 1/z² - 2×z×1/z = 36

=> z² + 1/z² = 36 + 2

=> z² + 1/z² = 38

Hence, z² + 1/z² = 38 is the required answer.

Answer 2

Answer:

38

Step-by-step explanation:

$z - \frac{1}{z } = 6$

$=> {(z - \frac{1}{z} )}^{2} = {6}^{2}$

$=> {z}^{2} - 2 \times z \times \frac{1}{z} + \frac{1}{ {z}^{2} } = 36$

$=> {z}^{2} + \frac{1}{ {z}^{2} } = 36 + 2$

$=> {z}^{2} + \frac{1}{ {z}^{2} } = 38$

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