Question

If a+1/a=√3 ,then a^17+(1/a)^17=?

Answer 1

hope it is helpful...all the best

Answer 2

Answer:

((√3 + i)/2)^17 + ((√3 - i)/2)^17

Step-by-step explanation:

(a + 1/a) = √3

squaring

a² + 1/a² +2a/a = 3

a² + 1/a²  = 3-2

a² + 1/a²  = 1

(a-1/a)² = a² + 1/a² - 2a/a

(a-1/a)² = 1 - 2

(a-1/a)² = -1

a - 1/a = +/- i  ( i = iota)

case 1  

a - 1/a =  i

2a = √3  + i

a = (√3 + i)/2

2/a = √3  - i

1/a =  (√3 - i)/2

a^17+(1/a)^17=((√3 + i)/2)^17 + ((√3 - i)/2)^17

Case 2

a - 1/a = - i

2a = √3  - i

a = (√3 - i)/2

1/2a = √3 + i

1/a = (√3 + i)/2

a^17+(1/a)^17=((√3 - i)/2)^17 + ((√3 + i)/2)^17

a^17+(1/a)^17= ((√3 + i)/2)^17 + ((√3 - i)/2)^17

Result is same as of case 1

so

a^17+(1/a)^17=((√3 + i)/2)^17 + ((√3 - i)/2)^17