Question

if x=3+2✓2 find x+1/x​

Answer 1

$3(2 - \sqrt{2)}$

Step-by-step explanation:

$x + \frac{1}{x} \\ 3 + 2 \sqrt{2} + \frac{1}{3 + 2 \sqrt{2} } \\ \frac{ {(3 + 2 \sqrt{2)} }^{2} + 1 }{3 + 2 \sqrt{2} } \\ \frac{9 + 8 + 12 \sqrt{2} + 1}{3 + 2 \sqrt{2} } \\ \frac{18 + 12 \sqrt{2} }{3 + 2 \sqrt{2} }$

Ratinalising denominator

$\frac{18 + 12 \sqrt{2} }{ 3 + 2 \sqrt{2} } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } \\ \frac{54 + 36 \sqrt{2} - 39 \sqrt{2} - 48 }{ {3}^{2} - {2 \sqrt{2} }^{2} } \\ \frac{6 - 3 \sqrt{2} }{9 - 8} \\ \frac{3(2 - \sqrt{2)} }{1} \\ 3(2 - \sqrt{2)}$