Question

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Question of class 9th

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

x = 3 + 2√2

1/x = 1/3 + 2√2

= (3 - 2√2)/(3 + 2√2)(3 - 2√2)

= (3 - 2√2)/ (3)² - (2√2)²

= (3 - 2√2)/ 9 - 8

= 3 - 2√2

x - 1/x = 3 + 2√2 - (3 - 2√2)

x - 1/x = 2√2 + 2√2

x - 1/x = 4√2

Here √2 is irrational number so, x - 1/x is also irrational.

Answer 2

Step-by-step explanation:

it would be Rational number.