Answer:
x + 1/x is rational
Step-by-step explanation:
Given: x= 3=2√2
Solution:
[tex]\frac{1}{x} = \frac{1}{3+2\sqrt{2} }[/tex] => [tex]\frac{1}{3+2\sqrt{2} }[/tex] × [tex]\frac{3-2\sqrt{2} }{3-2\sqrt{2} }[/tex] (RATIONALIZING)
[tex]\frac{3-2\sqrt{2} }{(3)^{2}-(2\sqrt{2}) ^{2} }[/tex] = [tex]3-2\sqrt{2}[/tex]
Therefore, x+1/x => [tex]3+ 2\sqrt{2} + 3- 2\sqrt{2} = 6[/tex]
Thus, it is rational.
Copyright © 2024 EHUB.TIPS team's - All rights reserved.
Answers & Comments
Verified answer
Answer:
x + 1/x is rational
Step-by-step explanation:
Given: x= 3=2√2
Solution:
[tex]\frac{1}{x} = \frac{1}{3+2\sqrt{2} }[/tex] => [tex]\frac{1}{3+2\sqrt{2} }[/tex] × [tex]\frac{3-2\sqrt{2} }{3-2\sqrt{2} }[/tex] (RATIONALIZING)
[tex]\frac{3-2\sqrt{2} }{(3)^{2}-(2\sqrt{2}) ^{2} }[/tex] = [tex]3-2\sqrt{2}[/tex]
Therefore, x+1/x => [tex]3+ 2\sqrt{2} + 3- 2\sqrt{2} = 6[/tex]
Thus, it is rational.