Question

if x=2+√3, find (x+1/x)3​

Answer 1

Step-by-step explanation:

x = 2 - √3--( 1 )

1/x = 1/( 2 - √3 )

= ( 2 + √3 ) / [ ( 2 - √3 )(2 + √3 ) ]

= ( 2 + √3 ) / [ 2² - ( √3 )² ]

= ( 2 + √3 ) / ( 4 - 3 )

= 2 + √3 ----( 2 )

x - 1/x

= 2 - √3 - ( 2 + √3 )

= 2 - √3 - 2 - √3

= - 2√3 ---( 3 )

Therefore ,

( x - 1/x )³ = ( - 2√3 )³

= - 24√3

I hope this helps you.

Answer 2

Answer:

Given that

x=2+√3

So,(x+1/x)3= (2+√3+1/2+√3)3

= [(2+√3)^2+1/2+√3]3

=[2^2+(√3)^2+2×2×√3+1/2+√3]3

= [4+3+4√3+1/2+√3]3

= [8+4√3/2+√3]3

= [4(2+√3)/2+√3]3

Now 2+√3 and 2+√3 will cancel out.

=(4)3

=12

hope it helps u....

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