Answer:
4
Step-by-step 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 + [tex]\sqrt{3}[/tex] is 2 - [tex]\sqrt{3}[/tex]
The conjugate of 2 - [tex]\sqrt{3}[/tex] is 2 + [tex]\sqrt{3}[/tex]
x = [tex]\frac{1(2-\sqrt{3)} }{(2+\sqrt{3})(2-\sqrt{3}) }[/tex] = [tex]\frac{2-\sqrt{3} }{4-3}[/tex] = 2 - [tex]\sqrt{3}[/tex]
y = [tex]\frac{1(2+\sqrt{3}) }{(2-\sqrt{3})(2+\sqrt{3}) }[/tex] = [tex]\frac{2+\sqrt{3} }{4-3}[/tex] = 2 + [tex]\sqrt{3}[/tex]
Thus
x + y = 2 - [tex]\sqrt{3}[/tex] + 2 + [tex]\sqrt{3}[/tex] = 4
