Question

If x=3-2√2 then check whether x+1/x is rational or irrational

Answer 1

Answer:

yes it is irrational

Step-by-step explanation:

Answer 2

Answer:

• Sum of x + 1/x is a rational number

Step-by-step explanation:

We are given that:

${\small{\tt{x = 3 - 2\sqrt2}}}$

We have to check whether

${\small{\tt{x + \dfrac{1}{x}}}}$

is a rational or irrational.

So,

${\small{\tt{x = 3 - 2 \sqrt2}}}$

${\small{\tt{\dfrac{1}{x} = \dfrac{1}{3 - 2\sqrt2} × \dfrac{3 + 2\sqrt2}{3+2\sqrt2}}}}$

${\small{\tt{\implies{\dfrac{1}{x} = 3 + 2\sqrt2}}}}$

Now ,

${\small{\tt{x + \dfrac{1}{x}}}}$

${\small{\tt{= 3{ \cancel {- 2\sqrt2 }}+ 3{ \cancel{ + 2\sqrt2}}}}}$

${\small{\tt{= 9}}}$

So, the sum of x + (1/x) is a rational number.