Question

If x=3+2 root 2 then find the value of x+1/x​

Answer 1

x = 3 + 2√2

x + 1/x

x = 3+2√2

1/x = 1/ 3+2√2

Rationalizing the denominator 3 + 2 root 2 we get,

1/X = 1/ 3 + 2 root 2 × 3 - 2 root 2/3 - 2root2

1/X = ( 3 - 2 root 2)/ ( 3 + 2 root 2) ( 3 - 2root2)

1/X = ( 3 - 2root 2) / (3)² - ( 2 root2)²

1/X = ( 3 - 2 root 2) / 9 -8

1/X = ( 3 - 2 root 2)

Therefore,

X + 1/X

=> ( 3 + 2 root 2 ) + ( 3 - 2 root 2)

=> ( 3 2 root 2)+ ( 2 root 2)

=> 6

Answer 2

$\mathfrak{\huge{Answer:}}$

Given is the value of x = $\tt{3 + 2\sqrt 2}$

We need to find the value of -》 $\tt{x + \frac{1}{x}}$

Put the value of x in this formula and then solve it :-

$\tt{3 + 2\sqrt 2 + \frac{1}{3 + 2\sqrt 2}}$

Now, we've written the equation. To get the value of $\tt{\frac{1}{3 + 2\sqrt 2}}$, we need to multiply and divide it by $\tt{3 - 2\sqrt 2}$.

Thus, the value of $\tt{\frac{1}{3 + 2\sqrt 2}}$ will be :-

$\tt{\frac{1}{3 + 2\sqrt 2}\times \frac{3 - 2\sqrt 2}{3 - 2\sqrt 2}}$

Solve this formed equation further

=》 $\tt{\frac{3 - 2\sqrt 2}{9 - 8}}$

Some more steps to go

=》 $\tt{3 - 2\sqrt 2}$

Rationalize them now :- $\tt{3 + 2\sqrt 2 + 3 - 2\sqrt 2}$

=》 $\boxed{\tt{6}}$

There's your answer!