Question

Pls solve this thanks

Answer 1

Step-by-step explanation:

x = (3 - √5)/2

=> 1/x = 2/(3 - √5) × (3 + √5)/(3 + √5)

=> [2(3 +√5)] / 9 - 5

=> 2(3 +√5) / 4

=> (3 + √5)/2

x + 1/x = (3 - √5)/2 + (3 + √5)/2

=> (3 - √5 +3 + √5)/2

=> 6/2 => 3

[x + 1/x]³ = x³ + 1/x³ + 3 * 1/x * x [ x + 1/x ]

=> 27 = x³ + 1/x³ + 3 [3 ]

=> 27 = x³ + 1/x³ + 9

=> x³ + 1/x³ = 18

now [x³ + 1/x³]² = x⁶ + 1/x⁶ + 2*x³*1/x³

=> 18² = x⁶ + 1/x⁶ + 2

therefore x⁶ + 1/x⁶ = 324 - 2 => 322