Question

x = 3-2√3. Then x+1/x​

Answer 1

Answer:

x=0.577,x+1/x=2.733

Step-by-step explanation:

x=3-2/squareroot 3

$\sqrt{3 = 1.732}$

x=1/1.732 or x=1/squareroot 3

If you calculate more you get in decimals

x+1/x=2.733

Answer 2

given

x=3 - 2√3

so we can write

$\frac{1}{x} = \frac{1}{3 - 2 \sqrt{3} }$

rationalizing denominator we get

$\frac{1}{x} = \frac{1}{3 - 2 \sqrt{3} } \times \frac{ 3 + 2 \sqrt{3} }{3 + 2 \sqrt{3} } \\ \\ \frac{1}{x} = \frac{3 + 2 \sqrt{2} }{9 - 12} = \frac{3 + 2 \sqrt{2} }{ - 3} \\ \\ \frac{1}{x} = - 1 - \frac{2 \sqrt{3} }{3}$

Now

$x + \frac{1}{x} = 3 - 2 \sqrt{3} - 1 - \frac{2 \sqrt{3} }{3} \\ \\ x + \frac{1}{x} = 2 - \frac{8 \sqrt{3} }{3}$