Question

e3 If x= 3 +
$\sqrt[2]{2}$
then find whether out x+
$\frac{1}{x}$
is rationas or
irrational​

Answer 1

Answer:

$x = 3 + \sqrt{2}$

$x + \frac{1}{x}$

$= (3 + \sqrt{2} )+ \frac{1}{(3 + \sqrt{2} ) }$

$= \frac{ {(3 + \sqrt{2}) }^{2} + 1 }{3 + \sqrt{2} }$

$= \frac{9 + 6 \sqrt{2} + 2 + 1 }{3 + {2}^{2} }$

$= \frac{ 12 + 6 \sqrt{2} }{3 + \sqrt{2} }$

Since, the above is irrational, therefore, x+1/x is also irrational.

Hope it helps (. ❛ ᴗ ❛.)