Question

a^2+1=a, then the value of a^12+a^6+1 is -?

Answer 1

Answer:

3

Step-by-step explanation:

a^2+1=a.

or,a^2+1/a=1

squaring both sides

(a^2)^2+(1/a)^2+2=1

(a^2)^2+(1/a)^2=-1

cubing both sides

a^6+1/a^6+3a^2×1/a^2(a^2+1/a)=(-1)^3

a^6+1/a^6+3×(-1)=-1

a^6+1/a^6+1=3

a^12+a^6+1

=a^6+1/a^6+1

=3