Question

x=2-√3 find the value of (x-1/x)^3+2(x+1/x)^2+(x+1/x)-100​

Answer 1

mk9120969

10.04.2018

Math

Primary School

answered • expert verified

If x=2-root 3,find the value of ( x-1 /x )whole

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.