Thread: Finding a value of an expression

1. Finding a value of an expression

$a, b, x, y$ are real numbers.
When they satisfy the equations $ax+by=3$, $ax^2+by^2=5$, $ax^3+by^3=9$, $ax^4+by^4=17$, find the value of $ax^5+by^5$.

2. I think I would be inclined to "cheat". Notice that 5- 3= 2, 9- 5= 4, and 17- 9= 8. If that pattern continues, the next number would be 17+ 16= 33.

3. Yeah, but how would you prove that?