Question

if x = √2 - 1 what is the value of x -1/x ?

Answer 1

if x = √2 - 1,
then 1/x = 1/(√2 - 1)
or, 1/x = (√2+1)/(√2-1)*(√2+1) = (√2+1)/( (√2)^2 - 1^2 ) = (√2+1)/(2-1) = √2 + 1

Thus,
x - 1/x = (√2 - 1) - (√2 + 1) = √2 - 1 - √2 - 1
or, x - 1/x = -2

Answer 2

Same answer as SathyaM711