Question

If x = 2 + V3, then the value of (x + 1/x) is​

Answer 1

Answer:

4

Step-by-step explanation:

Given

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

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

Rationalise the denominator of the fraction by multiplying the numerator/ denominator by the conjugate of the denominator.

The conjugate of 2 + $\sqrt{3}$ is 2 - $\sqrt{3}$ , thus

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

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

= 2 + $\sqrt{3}$ + 2 - $\sqrt{3}$

= 4