Question

2+✓3/2-✓3 solve the problem​

Answer 1

Answer:

$\frac{2 + \sqrt{3} }{2 - \sqrt{3} }$

rationalizing the denominator,,

$= \frac{(2 + \sqrt{3} )}{(2 - \sqrt{3}) } \times \frac{(2 + \sqrt{3}) }{(2 + \sqrt{3} )}$

by using formula , (a-b)(a+b) = a²-b² in the denominator.

$= \frac{( {2 + \sqrt{3} \: })^{2} }{ {(2)}^{2} - ( { \sqrt{3} })^{2} }$

$= \frac{ {(2 + \sqrt{3} })^{2} }{4 - 3}$

$= {(2 + \sqrt{3} })^{2}$

by the formula ,, (a+b)²= a²+b²+2ab

$= {4}^{2} + {( \sqrt{3} })^{2} + 2 \times 2 \times \sqrt{3}$

$= 16 + 3 + 4 \sqrt{3}$

$= 19 + 4 \sqrt{3}$