Question

if x=3+2√2 then the x+1/x is a rational number​

Answer 1

Answer:

yes it is rational

Step-by-step explanation:

x=3+2(2)1/2  

(1/x)=1/[3+2(2)1/2]  

Now rationalize

(1/x)=1/[3+2(2)^1/2]∗([3−2(2)^1/2]/[3−2(2)^1/2]  

(1/x)=[3−2(2)^1/2]/[32−2∗(2^1/2)^2]  

(1/x)=[3−2(2)^1/2]/[9−8]=3−2(2)1^/2  ]

x+(1/x)=3+2(2)^1/2+3−2(2)^1/2=6  

As 6 is rational hence x+1/x is rational

Answer 2

Answer:

yes, it is a rational number. because,

Step-by-step explanation:

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√2/9-8)

=(3+2√2) + (3-2√2)

=6 which can be written as p/q form(6/1)

therefore it is a rational number.

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