Question

If x=2+√3 and x+y=4,then find the simplest value of xy+1/xy?

if x=2+√3
then x+y=4
now,
putting the value of x is
x+y=4
2+√3+y=4
+y=4-2-√3
+y=2-√3

now, putting the value of x 2+√3 and y 2-√3 in equation xy+1/xy

xy+1/xy
(2+√3)(2-√3) + 1/(2+√3)(2-√3)

(4-2√3+2√3-3) + 1/4-2√3+2√3-3)

1 +1/1
2/1
2 is ans....​

Answer 1

Answer:

$x = 2 + \sqrt{3} \\ x + y = 4 \\ y = 4 - 2 - \sqrt{3} \\ = 2 - \sqrt{3} \\xy = (2 + \sqrt{3})(2 - \sqrt{3}) \\ by \: (a + b)(a - b) = {a}^{2} - {b}^{2} \\ xy = {2}^{2} - {( \sqrt{3} )}^{2} = 4 - 3 = 1 \\ xy + \frac{1}{xy} = 1 + \frac{1}{1} = 1 + 1 = 2$