Question

If x= 2- √3 , then value of ( x- 1/x )​

Answer 1

Step-by-step explanation:

1/x = 1/2-sqrt3

multiply numerator and denominator with 2+sqrt3

1/x = 2+sqrt3/ ( 2-sqrt3 × 2+sqrt3)

=2+sqrt3/2²-sqrt3²

= 2+sqrt3/(4-1)

= 2+sqrt3

x-1/x = 2-sqrt3 -2-sqrt3 = -2 sqrt 3

Answer 2

Given :

• x= 2- √3

To find :

• x- 1/x

Solution :

$\sf \implies x= 2- \sqrt{3}$

$\sf \implies \dfrac{1}{x} = \dfrac{1}{2- \sqrt{3} }$

$\sf \implies \dfrac{1}{x} = \dfrac{1}{2- \sqrt{3} } \times \dfrac{2 + \sqrt{3}}{2 + \sqrt{3} }$

$\sf \implies \dfrac{1}{x} = \dfrac{2 + \sqrt{3}}{ {(2)}^{2} - {(\sqrt{3})}^{2} }$

$\sf \implies \dfrac{2 + \sqrt{3}}{ {(2)}^{2} - {(\sqrt{3})}^{2} } = \dfrac{2 + \sqrt{3}}{ 4 - 3 }$

$\sf \implies \dfrac{2 + \sqrt{3}}{ 4 - 3 } = \dfrac{2 + \sqrt{3}}{ 1 }$

$\sf \implies \dfrac{1}{ x } = \dfrac{2 + \sqrt{3}}{ 1 }$

$\sf \implies x - \dfrac{1}{ x } = 2 - \sqrt{3} - 2-\sqrt{3}$

$\sf \implies x - \dfrac{1}{ x } = 2 \sqrt{3}$

Answer : -2√3