If x= 3+2√2, check whether x +1/x is rational or irrational.
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Hey ya!
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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