Question

if x=2root3+2root2 find:
1/x
x+1/x

Answer 1

Answer:

$x = 2 \sqrt{3} + 2 \sqrt{2} \\ \frac{1}{x} = \frac{1}{2 \sqrt{3} + 2 \sqrt{2} } \times \frac{2 \sqrt{3} - 2 \sqrt{2} }{2 \sqrt{3} - 2 \sqrt{2} } \\ \: \: \: \: = \frac{2 \sqrt{3} - 2 \sqrt{2} }{12 - 8} = \frac{2 \sqrt{3} - 2 \sqrt{2} }{4} \\ \: \: \: \\ x + \frac{1}{x} = 2 \sqrt{3} + 3 \sqrt{2} + \frac{2 \sqrt{3} - 2 \sqrt{2} }{4} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{8 \sqrt{3} + 12 \sqrt{2} + 2 \sqrt{3} - 2 \sqrt{2} }{4}$