#This one
hard narwhal
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midnight island
you can probably just synthetic divison it tbh
hard narwhal
how do you do that
midnight island
how do you do that
wait what skills do you know/are expected to solve it with
hard narwhal
10th grade maths
hard narwhal
like remainder theorom
midnight island
how would your teacher tell you to solve these then, what
hard narwhal
idk, he just gave it as hw, like its non-routine maths
scenic crystal
The roots of x^2 - x - 1 are φ and -1/φ. So, the given polynomial must also be 0 for both φ and -1/φ, which leads to the following system:
aφ^17 + bφ^16 + 1 = 0
-a/φ^17 + b/φ^16 + 1 = 0
It's convenient to multiply the second equation by -φ^17 first.
aφ^17 + bφ^16 + 1 = 0
a - bφ - φ^17 = 0
Now, try solving for a and b, and then simplifying the answer by repeatedly applying the property φ^2 = φ + 1. Alternatively, you can use the relation φ^n = F(n)φ + F(n - 1), where F(n) is the n-th Fibonacci number, if you remember them quite far.
hard narwhal
whats the fibonacci number?