Question

if x =3-2√2 find x+1/x

Answer 1

Given x=3-2√2
x+1/x=3-2√2+1/(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√2)²]
⇒3-2√2+(3+2√2)/(9-8)
⇒3-2√2+(3+2√2)/1
⇒3-2√2+3+2√2
⇒6.
∴x+1/x=6

Answer 2

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