Question

if X=3+2√2 then find the value of
X+1/X​

plz answer faaaaaaaast

Answer 1

Answer:

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

2

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

x+

x

1

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

\begin{gathered}\tt{3 + 2\sqrt 2 + \frac{1}{3 + 2\sqrt 2}}\\\end{gathered}

3+2

2

+

3+2

2

1

Now, we've written the equation. To get the value of \begin{gathered}\tt{\frac{1}{3 + 2\sqrt 2}}\\\end{gathered}

3+2

2

1

, we need to multiply and divide it by \tt{3 - 2\sqrt 2}3−2

2

.

Thus, the value of \begin{gathered}\tt{\frac{1}{3 + 2\sqrt 2}}\\\end{gathered}

3+2

2

1

will be :-

\begin{gathered}\tt{\frac{1}{3 + 2\sqrt 2}\times \frac{3 - 2\sqrt 2}{3 - 2\sqrt 2}}\\\end{gathered}

3+2

2

1

×

3−2

2

3−2

2

Solve this formed equation further

=》 \begin{gathered}\tt{\frac{3 - 2\sqrt 2}{9 - 8}}\\\end{gathered}

9−8

3−2

2

Answer 2

Step-by-step explanation:

X=3+2√2

$x + \frac{1}{x} = 3 + 2 \sqrt{2} + \frac{1}{3 + 2 \sqrt{2} }$

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

$=( 9 + 8 + 12 \sqrt{2} + 1) \div (3 + 2 \sqrt{2} )$

$= \frac{(18 + 12 \sqrt{2} )}{(3 + 2 \sqrt{2)} }$

$= \frac{18 + 2 \sqrt{2} }{3 + 2 \sqrt{2} } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} }$

$= \frac{54 - 36 \sqrt{2 } + 6 \sqrt{2} - 8 }{ ({3}^{2} - {2 \sqrt{2} }^{2}) }$

$= \frac{46 - 30 \sqrt{2} }{9 - 8}$

$= 46 - 30 \sqrt{2}$