Question

If x=3-2√2 find the value of x+1/x

Answer 1

Answer:

Given x = 3+2√2

x +1/x

= 3+2√2 + 1 / 3+2√2

= 3+2√2 + 3-2√2 / 3+2√2(3-2√2)

= 3+2√2 + 3-2√2 / 3² - (2√2)²

= 3+2√2 + 3-2√2/9-8

= 3+2√2 + 3-2√2

= 6 Which can be written in p/q forrm. (6/1)

Therefore it's a rational number!.

Step-by-step explanation:

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Answer 2

Answer:

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