# If X = 2 + √ 3 , Find the Value of X + 1 X . - Mathematics

If $x = 2 + \sqrt{3}$ ,  find the value of $x + \frac{1}{x}$.

#### Solution

Given that, x= 2+sqrt3 hence

$\frac{1}{x}$  is given as

. 1/x = 1/(2+sqrt3)We are asked to find  x +1/x

We know that rationalization factor for 2+sqrt3 is2-sqrt3 . We will multiply each side of the given expression  1/(2+sqrt3) by, 2-sqrt3 to get

. 1/x = 1/(2+sqrt3) xx(2-sqrt3)/(2-sqrt3)

= (2-sqrt3)/((2)^2-(sqrt3)^2)

= (2-sqrt3)/(4-3)

=2-sqrt3

Therefore,

x+1/x = 2+sqrt3 +2 - sqrt3

=4

Hence value of the given expression is 4 .

Concept: Operations on Real Numbers
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.3 | Q 7 | Page 16

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