Question

if x=2√3+2√2 find 1/x and (x+(1/x))²......Please answer as soon as possible

Answer 1

Given x = 3+2√2

x +1/x

= 3+2√2 + 1 / 3+2√2

= 3+2√2 + 3-2√2 / 3+2√2(3-2√2)

= 3+2√2 + 3-2√2 / 3² - (2√2)²

= 3+2√2 + 3-2√2/9-8

= 3+2√2 + 3-2√2

= 6 Which can be written in p/q forrm. (6/1)

Therefore it's a rational number!.


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Answer 2

$\frac{2 \sqrt{3} - 2 \sqrt{2} }{4} \\ common \: factor \: \\ so \\ \frac{ \sqrt{3} - \sqrt{2} }{2}$