Question

If a^2 - 5a -1 = 0 and a is not equal to zero find a - 1/a, a+1/a and a^2 - 1/a^2

Answer 1

Answer:

Step-by-step explanation:

a^2-1=5a

divide by a on both sides

a-1/a=5

and

a^2+1/a^2-2=25

a^2+1/a^2=27

now

(a+1/a)^2=a^2+1/a^2+2a*1/a=27+2=29

a+1/a=sqrt(29)

a^2-1/a^2=(a+1/a)(a-1/a)=(sqrt(29))(5)=5sqrt(29)