Question

If x =5-√3/5+√3. and y= 5+√3/5-√3,show that x² - y ²= -10√3/11

Answer 1

Hiii. .....friend

The answer is here,

$= > \: x = \frac{5 - \sqrt{3} }{5 + \sqrt{ 3} }$

$= > \: \frac{5 - \sqrt{3} }{5 + \sqrt{3} } \times \frac{5 - \sqrt{3} }{5 - \sqrt{3} }$


$= > \: \frac{25 + ( { \sqrt{3})}^{2} - 10 \sqrt{3} }{ {5}^{2} - { \sqrt{3} }^{2} }$

$= > \: \frac{28 - 10 \sqrt{3} }{16}$

$y = \frac{5 + \sqrt{3} }{5 - \sqrt{3} }$

$= > \: \frac{5 + \sqrt{3} }{5 - \sqrt{3} } \times \frac{5 + \sqrt{3} }{5 + \sqrt{3} }$

$= > \: \frac{28+ 10 \sqrt{3} }{16}$

$= > \: {x}^{2} - {y}^{2} = ( { \frac{28 - 10 \sqrt{3} }{16} )}^{2} - ({ \frac{28+ 10 \sqrt{3} }{16} )}^{2}$

This is in the form ,

$= > \: {a}^{2} - {b}^{2} = (a + b)(a - b)$

$= > \: ( \frac{28- 10 \sqrt{3} + 28 + 10 \sqrt{3} }{16} )( \frac{28- 10 \sqrt{3} - 28 - 10 \sqrt{3} }{16} )$

$= > \: ( \frac{56}{16} )( \frac{ - 20\sqrt{3} }{16} )$

$= > \: \frac{ - 35 \sqrt{3} }{8}$

:-(Hope it helps u.