Question

If x= 2-√3, then x + 1/x equals a) 4 b) 2+√3 c) 4-√3 d) 1/(2+√3)​

Answer 1

Explanation:

To find x + 1/x, we need to first find the value of x.

Given, x = 2-√3

To simplify x + 1/x, we need to find the value of 1/x.

1/x = 1/(2-√3)

Multiplying the numerator and denominator by the conjugate of the denominator, we get:

1/x = (2+√3)/(2-√3)(2+√3)

1/x = (2+√3)/(4-3)

1/x = 2+√3

Now, substituting the values of x and 1/x, we get:

x + 1/x = (2-√3) + (2+√3)

x + 1/x = 4

Therefore, the answer is option a) 4.