Question

if x=3+2root2findx-1/x

Answer 1

x=3+2√2
1/x = 1/(3+2√2)
rationalizing the denominator,
1/(3+2√2) × (3-2√2)/(3-2√2)
(3-2√2)/(3)²-(2√2)²
3-2√2/(9-8)
3-2√2/1 = 3-2√2
x-1/x = 3+2√2-(3-2√2)
3+2√2-3+2√2
4√2 is the answer
hope this helps

Answer 2

x = 3+2√2

$\frac{1}{x}$ = 1/3+2√2 × 3-2√2/3-2√2
= (3-2√2)/{3²-(2√2)²}
= (3-2√2)/9-4(2)
= (3-2√2)/9-8
= (3-2√2)/1
∴ $\frac{1}{x}$ = 3-2√2

x - $\frac{1}{x}$ = 3+2√2 - (3-2√2)
= 3+2√2-3+2√2
= 4√2