Question

X=t="\frac{1}{2+\sqrt{3} }" align="absmiddle" class="latex-formula">
y=$\frac{1}{2-\sqrt{3} }$

x+y=

Answer 1

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

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

x = $\frac{1(2-\sqrt{3)} }{(2+\sqrt{3})(2-\sqrt{3}) }$ = $\frac{2-\sqrt{3} }{4-3}$ = 2 - $\sqrt{3}$

y = $\frac{1(2+\sqrt{3}) }{(2-\sqrt{3})(2+\sqrt{3}) }$ = $\frac{2+\sqrt{3} }{4-3}$ = 2 + $\sqrt{3}$

Thus

x + y = 2 - $\sqrt{3}$ + 2 + $\sqrt{3}$ = 4