X=(1)/(2+√(3) ) y=(1)/(2-√(3) ) x+y=

Question

X=
`(1)/(2+√(3) )`
y=
`(1)/(2-√(3) )`

x+y=

Answer 1

4

Explanation:

Simplify x and y by rationalising the denominator of both

To rationalise the denominator multiply the numerator/ denominator by the conjugate of the denominator.

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

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

x =
`(1(2-√(3)) )/((2+√(3))(2-√(3)) )` =
`(2-√(3) )/(4-3)` = 2 -
`√(3)`

y =
`(1(2+√(3)) )/((2-√(3))(2+√(3)) )` =
`(2+√(3) )/(4-3)` = 2 +
`√(3)`

Thus

x + y = 2 -
`√(3)` + 2 +
`√(3)` = 4