SOLUTION: if a^2 + 1 = a, then the value of a^12 + a^6 + 1 is

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Question 782806: if a^2 + 1 = a, then the value of a^12 + a^6 + 1 is
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
a%5E12+%2B+a%5E6+%2B+1
= %28a%5E2%29%5E6+%2B+a%5E6+%2B+1
= %28a-1%29%5E6+%2B+a%5E6+%2B+1
= %28%28a-1%29%5E2%29%5E3+%2B+a%5E6+%2B+1
= %28a%5E2%2B2a%2B1%29%5E3+%2B+a%5E6+%2B+1
= %28a%2B2a%29%5E3+%2B+a%5E6+%2B+1
= %283a%29%5E3+%2B+a%5E6+%2B+1
= 27a%5E3+%2B+%28a%5E2%29%5E3+%2B+1
= 27a%5E3+%2B+%28a-1%29%5E3+%2B+1
= 27a%5E3+%2B+a%5E3-3a%5E2%2B3a-1+%2B+1
= 28a%5E3+-3a%5E2%2B3a
= 28a%5E3+%2B3%28-a%5E2%2Ba%29
= 28a%5E3+%2B3%281%29
= 28a%5E3+%2B3