Question

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

Answer 1

4

Explanation:

Given

x +
`(1)/(x)` ← substitute x = 2 +
`√(3)`

= 2 +
`√(3)` +
`(1)/(2+√(3) )`

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

The conjugate of 2 +
`√(3)` is 2 -
`√(3)` , thus

= 2 +
`√(3)` +
`(2-√(3) )/((2+√(3) )(2-√(3)) )`

= 2 +
`√(3)` +
`(2-√(3) )/(4-3)`

= 2 +
`√(3)` + 2 -
`√(3)`

= 4