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

1. 2
2. 3
3. -3
4. 1
Anurag Mishra Professor Asked on 1st August 2015 in

Explanation:-
a2 + 1 = a
Both side divide by a,
a2/a + 1/a = a/a
a + 1/a + 1
On squaring of both sides,
(a + 1/a)2 = 12
a2 + 1/a2 + 2 x a x 1/a = 1
a2­ + 1/a2 + 2  = 1
a2 + 1/a2 = 1 – 2 = -1                                …………………….. (1)
On cubing of both sides,
(a2 + 1/a2 )3 = ( – 1)3
(a2)3 + (1/a2)3  + 3 x a2 x 1/a2 (a2 + 1/a2) = (-1) x (-1) x (- 1)
a6 + 1/a6 + 3(a2 + 1/a2) = – 1
a6 + 1/a6 + 3 (-1) = – 1
a6 + 1/a6 + 1 =  3                                     …………………….. [From equation (1)]
(a12 + 1 + a6)/a6 = 3
a12 + a6 + 1 = 3
Hence, the answer is (2) 3.

Anurag Mishra Professor Answered on 1st August 2015.

(a^12+1+a^6)/a^6=3
a^12+1+a^6=3*a^6
how it became 3 sir please explain……….

sree Default Answered on 1st July 2016.

a2 +1 = a

a2 –a +1 =0

multiply by (a+1) on both side

(a+1)( a2 –a +1) =0

a3 + 13 = 0    ( Since a3 + 13  = (a+1)( a2 –a +1)

a3 = -1

Now put the value of a3 in given expression

a12 + a6 +1= (-1)4 + (-1)2 + 1 =1+1+1 = 3

ramsingh Default Answered on 12th December 2016.

a2 +1 = a

a2 –a +1 =0

multiply by (a+1) on both side

(a+1)( a2 –a +1) =0

a3 + 13 = 0    ( Since a3 + 13  = (a+1)( a2 –a +1)

a3 = -1

Now put the value of a3 in given expression

a12 + a6 +1= (-1)4 + (-1)2 + 1 =1+1+1 = 3

ramsingh Default Answered on 12th December 2016.