The most basic approach here is to simplify as much as possible. Therefore you do:
(1/2 x 8x + 1/2 x 4) - (1/3 x 3x + 1/3 x 9) =17
(4x + 2) - (x + 3) = 17
4x + 2 - x - 3 = 17
3x - 1 = 17
Then you pass the one on the other side which gives:
3x = 17 + 1
3x = 18
Finally divide everything by 3:
x = 6
1.11111, 1.111111, 1.1111111
The first two are given to you, and . Use the recursive formula to get the 3rd term; then use the 2nd and 3rd terms to get the 4th; and so on.
Since the <em>n</em>-th Lucas number is the sum of the previous two Lucas numbers, you have