Question

if x=3+2√2 find the value of x-1/x​

Answer 1

Given, x =3-2√2

We have to find the value of x+(1/x)

Taking lcm,

x+(1/x) = (x²+1)/x

Replacing the value of x

= {(3-2√2)²+1}/3-2√2

{(3-2√2)²} can be written as (3-2√2)(3-2√2) for our convenience

= {(3-2√2)(3-2√2)+1}/3-2√2

By rationalizing,

= [{(3-2√2)(3-2√2)+1}/3-2√2] × [3+2√2/3+2√2]

= [(3+2√2)(3-2√2)(3-2√2) + 1(3-2√2)] / (3-2√2)(3+2√2)

We know that (3-2√2)(3-2√2) = 9-8 = 1

Placing it in (3+2√2)(3-2√2)

= 1(3-2√2)+1(3-2√2)/1

= 3-2√2+3-2√2

= 3+3

= 6

therefore, the value of x+(1/x) = 6

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