Question

If x=3-2√2 find the value of x-1/x

Answer 1

x = 3-2√2

1/x = 1/3-2√2

= 1/3-2√2*3+2√2/3+2√2

= 3+2√2/3²-(2√2)²

= 3+2√2/9-8

= 3+2√2/1 = 3+2√2

x+1/x = 3-2√2+3+2√2 = 6                                (∵2√2 and-2√2 would cut each other)