Question

if z+1/z=√3 then find z^3+(1/z)^3​

Answer 1

Answer:

3√3

Step-by-step explanation:

$z + \frac{1}{z} = \sqrt{3} \\ \\ {z}^{3} + { \frac{1}{z} }^{3} = \\ \\ (z ^{3} + \frac{1}{z} ^{3} ) = (z + \frac{1}{z}) \times ( {z}^{2} + \frac{1}{z} ^{2} - (z \times \frac{1}{z} ) \\ \\ = \sqrt{3 } \times ( {z}^{2} + \frac{1}{z} ^{2} - 1+3)$

$(z² + \frac{1}{z} ) ^{2} = {z}^{2} + \frac{1 }{z }^{2} + 2$

(√3)(3)=3√3