Question

If a2 + 1 = a, then the value of a12 + a6 + 1 is

(a) 2
(b) 3
(c) -3
(d) 1
someone please explain in short​

Answer 1

Answer:

b

Step-by-step explanation:

a²+1 =a

a²-a+1=0

multiply both sides with (a+1)

(a+1)(a²-a+1)=0 x (a+b)

(a+1)(a²-(a*1)+1²) = 0 as a³+b³=(a+b)(a²-ab+b²)

a³+1³=0

a³=-1³

a=-1

a12=(-1)^12=1

a^6=(-1)^6=1

a12+a6+1= 1+1+1 =3