If x= 3+2√2,then find the value of x+1\x

1.	If x= 3+2√2,then find the value of x+1\x
Answer» Given: x=3+2√2 To find the value of, $\sf{x + \frac{1}{x} } \\ \\$ Here, We find the value of 1/x and then,add it with that of x. THUS, deriving the required value. Now, What is rationalising? Rationalising is a mathematical TOOL or procedure which is applied to REMOVE the RADICAL signs EITHER by multiplying or dividing. So, $\sf{ \frac{1}{x} = \frac{1}{3 + 2 \sqrt{2} } } \\ \\ \: \: \: \: \: = \sf{ \frac{1}{3 + 2 \sqrt{2} } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } } \\ \\ \: \: \: \: = \sf{\frac{3 - 2 \sqrt{2} }{3 {}^{2} - 2 \sqrt{2 {}^{2} } }} \ \\ \\ \: \: \: = \sf{\frac{3 - 2 \sqrt{2} }{9 - 8}} \\ \\ \implies \: \sf{ \frac{1}{x} = 3 - 2 \sqrt{2} }$ On adding both the term, (3+2√2)+(3-2√2) =3+3 =6 $\sf{6 \: is \: the \: value \: of \: x + \frac{1}{x} } \\ \\$

Answer»

Given:

x=3+2√2

To find the value of,

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

Here,

We find the value of 1/x and then,add it with that of x. THUS, deriving the required value.

Now,

What is rationalising?

Rationalising is a mathematical TOOL or procedure which is applied to REMOVE the RADICAL signs EITHER by multiplying or dividing.

So,

$\sf{ \frac{1}{x} = \frac{1}{3 + 2 \sqrt{2} } } \\ \\ \: \: \: \: \: = \sf{ \frac{1}{3 + 2 \sqrt{2} } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } } \\ \\ \: \: \: \: = \sf{\frac{3 - 2 \sqrt{2} }{3 {}^{2} - 2 \sqrt{2 {}^{2} } }} \ \\ \\ \: \: \: = \sf{\frac{3 - 2 \sqrt{2} }{9 - 8}} \\ \\ \implies \: \sf{ \frac{1}{x} = 3 - 2 \sqrt{2} }$