Question

Q. if x=2+root 3, then 1/x is equal to-​

Answer 1

Answer:

2-root 3

Step-by-step explanation:

Complete explanation in the pic..

Answer 2

x = 2 + √3

then,

$\frac{1}{x} = \frac{1}{2 + \sqrt{3} }$

$\mathfrak\red{rationalising\:the\:denominator}$

= $\frac{1}{2 + \sqrt{3} } \: \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} }$

= $\frac{2 - \sqrt{3} }{2 {}^{2} - \sqrt{3 {}^{2} } }$

= $\frac{2 - \sqrt{3} }{4 - 3}$

= $\frac{2 - \sqrt{3} }{1}$

= $2 - \sqrt{3}$