Question

c) If x = 2√3 +2√2,find (X+1/X)​

Answer 1

Answer:

x = 2√3 +2√2

$x + \frac{1}{x} = \frac{ {x}^{2} + 1 }{x}$

$\frac{12 + 8 + 4 \sqrt{6} }{2 \sqrt{3} + 2 \sqrt{2} }$

$= \frac{20 + 4 \sqrt{6} }{2 \sqrt{3} + 2 \sqrt{2} }$

$= \frac{10 + 2 \sqrt{6} }{ \sqrt{3} + \sqrt{2} }$

Rationalize

$= (10 + 2 \sqrt{6}) \times ( \sqrt{3} - \sqrt{2} )$

$= (10 \sqrt{3} - 10 \sqrt{2} + 6 \sqrt{2 } - 4 \sqrt{3} )$

$= 6 \sqrt{3} - 4 \sqrt{2}$

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