Question

If x=2root 3+ 2 root 2 find x+1/x

Answer 1

Answer:

(x+1/x) = (9√3 + 7√2)/4

Step-by-step explanation:

Since x = 2√3 + 2√2

Therefore,

1 / x = 1 / 2√3 + 2√2

Rationalizing it we get

= 1 / 2√3 + 2√2 * 2√3 - 2√2 / 2√3 - 2√2

= 2√3 - 2√2 / 4

We take 2 common from the numerator Therefore

= 2(√3 - √2) / 4

= √3 - √2 / 2

Now,

(x + 1/x) = 2√3 + 2√2 + (√3-√2 / 4)

Taking LCM as 4

We get

(8√3 + 8√2 + √3 - √2)/4

Therefore

(9√3 + 7√2)/4

Answer 2

Answer:

(x+1/x)= 5√3+3√2/2

Step-by-step explanation:

Since,

x = 2√3 + 2√2

1 / x = 1 / 2√3 + 2√2

On rationalizing the denominator, we get

= 1 / 2√3 + 2√2 * 2√3 - 2√2 / 2√3 - 2√2

= 2√3 - 2√2 / 4

On taking 2 common from the numerator we get,

= 2(√3 - √2) / 4

= √3 - √2 / 2

Now,

(x + 1/x) =

(2√3 + 2√2) + (√3-√2 / 2)

Taking LCM as 2, we get

(4√3 + 4√2 + √3 - √2)/2

(4√3+√3+4√2-√2)/2

Thus, the answer is=

5√3+3√2/2