Question

If x = 1 + √2 then show that (x - 1 \ x)³ = 8

Answer 1

Answer:

1/x=1/(1+√2)=√2-1)/{√2+1)(√2-1)}

=(√2-1)/(2-1)=√2-1

{(x-1/x)}^3={(√2+1)-(√2-1)}^3

={√2+1-√2+1)^3=(2)^3=8