Question

If x= 2+√3, find the value of x-1/x.​

Answer 1

Answer:

2√3

Step-by-step explanation:

x = 2 + √3

1/x = 1 / ( 2 + √3 )

Rationalise by multiplying '2-√3' with numerator and denominator

⇒ 1/x = 1*(2 - √3)/(2 + √3)*(2 - √3)

         = (2 - √3)/ 2² - (√3)²      [∵ (a+b)(a-b) = a² - b²]

         = (2 - √3) / 4 - 3 = 2 - √3

∴ x - 1/x = 2 + √3 - (2 - √3)

            = 2 + √3 - 2 + √3

            = 2√3

Answer 2

Answer:

2√3

Step-by-step explanation:

x=2+√3

1/x=1/2+√3

by rationalising

1/x=1/2+√3*2-√3/2-√3

1/x=2-√3/(2)^2-(√3)^2

as{(a+b)(a-b)=a^2-b^2}

1/x=2-√3/4-3

1/x=2-√3

so,x-1/x=2+√3-(2-√3)

so,x-1/x=2+√3-2+√3

so,x-1/x=2√3