Question

If x= 2+root 3 then find value of x-1/x

Answer 1

Step-by-step explanation:

\sf{GIVEN:-}

x = 2 + √3

1/x = 1/(2 + √3) * (2 - √3)/(2 - √3)

1/x = (2 - √3)/(4 - 3)

[ (a - b)(a + b) = (a² - b²) ]

1/x = (2 - √3)

now,

x + 1/x = (2 + √3) + (2 - √3)

x + 1/x = 2 + 2 + √3 - √3

x + 1/x = 4

Hope it Helps.....!

Answer 2

Answer:

2√3

Step-by-step explanation:

⇒ x = 2 + √3

⇒ 1/x = 1/( 2 + √3 )

  Multiply as well as divide( RHS ) by 2 - √3:

⇒ 1/x = ( 2 - √3 ) / ( 2 + √3 )( 2 - √3 )

⇒ 1/x = ( 2 - √3 ) / [ (2)^2 - (√3)^2 ]

⇒ 1/x = ( 2 - √3 ) / ( 4 - 3 )

⇒ 1/x = ( 2 - √3 )/1

⇒ 1/x = 2 - √3

Hence,

       ⇒ x - 1/x

       ⇒ 2 + √3 - ( 2 - √3 )

       ⇒ 2 + √3 - 2 + √3

       ⇒ √3 + √3

        ⇒ 2√3