let an= t4 than an-2= t2 and an-4=1
solving the given equation as-- > characteristics equation -- >
t4=8t2-16
t4-8t2+16=0
(t2-4)2=0
(t-2)2 (t+2)2 =0
t= +2 and t= -2
since the roots are real and unequal and in the second order-->
an= (A1 +A2x)(2)n + (B1 +B2x) (-2)n
Answer