Question

If x=2 + √3, then x + 1/x =

a. 4
b. -5
c. -4
d. 5​

Answer 1

Answer:

(a) 4.

Step-by-step explanation:

Given;

x = 2 + √3

1/x = 1/(2+√3)

[ Rationalise 1/(2+√3) ]

=> 1/(2+√3) × (2-√3)/(2-√3)

=> (2-√3)/(2+√3)-(2+√3)

=> 2-√3/1 = 2-√3

therefore 1/x = 2 - √3

we've to find the value of x + 1/x

=> ( 2 + √3 ) + ( 2 - √3)

=> 4 + √3 - √3

=> 4..

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Answer 2

given

$x = 2 + \sqrt{3}$

we can Write

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

rationalizing denominator we get

$\frac{1}{x} = \frac{2 - \sqrt{3} }{4 - 3} \\ \\ \frac{1}{x} = 2 - \sqrt{3}$

Now

$x + \frac{1}{x} = 2 + \sqrt{3} + 2 - \sqrt{3} \\ \\ x + \frac{1}{x} = 4$