Question

If a²-2a-1=0, then find: a-1/a​

Answer 1

Answer:

a^2-2a+1=2

(a-1)^2=(√2)^2

a-1=+ √2 and a-1=-√2

a=√2+1 and a=1-√2

For a=√2+1, 1/a=1/(√2+1)=(√2-1)/{(√2+1)(√2-1)}=√2-1

a-(1/a)=√2+1-(√2-1)=2

For a=1-√2, 1/a=1/(1-√2)=(1+√2)/{(1-√2)(1+√2)}=

1+√2/(1-2)=-1-√2

a-1/a=1-√2-(-1-√2)=2