Question

If x=2+√3, then x+1



=

a. 5 b. 4 c. -4 d. -5​

Answer 1

Answer:

a.5

Step-by-step explanation:

2+root3+1

= 3+root3

=3+1.732

=4.732 [aprox=5]

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

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