Question

If a^2-1/a=1 find the value of a^6-1/a

Answer 1

Answer:

2(sqrt(5) -3) or 2(sqrt(5)) +6

Step-by-step explanation:

(a^2 -1)/a = 1

=> (a^2 -1) = a

=> a^2 -a - 1= -

a= 1/2 - sqrt(5)/2 or 1/2 + sqrt(5)/2

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(a^6 -1)/a

=> ((1/2 -sqrt(5)/2)^6 - 1 )/(1/2 -sqrt(5)/2) => 2(sqrt(5) -3)

or

=> ((1/2 +sqrt(5)/2)^6 - 1 )/(1/2 +sqrt(5)/2) => 2(sqrt(5)) +6