Question

ifx=2+√3 then simplified form of 1byx is​

Answer 1

Answer:

If x= 2+sqrt3

then

1/x=2-sqrt3 (by rationaliztion)

then (x+1/x)^2 = X^2+(1/X)^2 +2*x*(1/X)

that is (2+sqrt3 +2-sqrt3)^2=x^2 +(1/x)^2+2

4^2 -2=x^2+(1/x)^2

i.e, 14 is the answer

Answer 2

${\huge{\underline{\underline{\sf {\mathfrak{Answer}}}}}}$

${\underline{\underline{\rm {Given:}}}}$

• $x = 2 + \sqrt3$
• $\dfrac{1}{x} = ?$

${\underline{\underline{\rm {Solution:}}}}$

$x = 2 + \sqrt3$

$\dfrac{1}{x} = \dfrac{1}{2 + \sqrt3}$

$\underline{\underline{\rm{Rationalizing:}}}$

$\dfrac{1}{x} = \dfrac{1}{2 + \sqrt3} \times \dfrac{2 - \sqrt3}{2- \sqrt3}$

$\dfrac{1}{x} = \dfrac{2 - \sqrt3}{2^2 - (\sqrt3)^2}$

$\dfrac{1}{x} = \dfrac{2 - \sqrt3}{4 - 3}$

$\boxed{\implies{\boxed{\dfrac{1}{x} = 2 - \sqrt3}}}$