@SSunakasusaikou you can square both side and get rid of absolute value then the problem become a 5-degree polynomial <= 0 which show first term is zero a=0 then second term become zero so third term is zero b=0 then c=0 by similar step
@isinnthetai First we know a_1=1 a_2=6.
then, for n>=3, a_{n+1} = 6*a_n-a_{n-1}
deduce b_n = a_{n+1} -(3+2*2^[1/2])a_n
for n>=2 b_{n+1} = (3-2*2^[1/2])b_n, with b_1 = 17 - 12*2^[1/2]
so we can easily derive a formula for b_n
then use basic arithmetic you can get a_n
( Too long