x=3+2√2 whether x+1/x is rational or irrational
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Given that,
x = 3 + 2√2
So, 1/x = 1/(3 + 2√2)
= (3 - 2√2)/{(3 + 2√2)(3 - 2√2)}
= (3 - 2√2)/(9 - 8)
= 3 - 2√2
∴ x + 1/x
= 3 + 2√2 + 3 - 2√2
= 6,
which is a rational number.
Hope it helps! (:
Given that,
x = 3 + 2√2
So, 1/x = 1/(3 + 2√2)
= (3 - 2√2)/{(3 + 2√2)(3 - 2√2)}
= (3 - 2√2)/(9 - 8)
= 3 - 2√2
∴ x + 1/x
= 3 + 2√2 + 3 - 2√2
= 6,
which is a rational number.
Hope it helps! (:
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