Question

Friend Simply this

1/√3 +√2 -1/√2 -√3
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Answer 1

$\sf\large\underline\blue{Given:-}$

$\\ = { \bold{ \dfrac{1}{ \sqrt{3} + \sqrt{2} } - \dfrac{1}{ \sqrt{2} - \sqrt{3}}}}$

$\sf\large\underline\blue{To\: Simplify :-}$

$\\ = { \bold{ \dfrac{1}{ \sqrt{3} + \sqrt{2} } - \dfrac{1}{ \sqrt{2} - \sqrt{3}}}}$

$\sf\large\underline\blue{Formula\: used:-}$

• a² - b² = ( a + b) ( a - b)

$\sf\large\underline\blue{Solution:-}$

$\small{\underline{\sf{\green{Let-}}}}$

the function be

$↦ { \bold{x = \dfrac{1}{ \sqrt{3} + \sqrt{2} } - \dfrac{1}{ \sqrt{2} - \sqrt{3}}}}$

( Rationalization of denominator )

$↦ { \bold{x = \dfrac{1}{ \sqrt{3} + \sqrt{2}} \times \dfrac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} - \sqrt{2} } - \left \{\dfrac{1}{ \sqrt{2} - \sqrt{3}} \times \dfrac{ \sqrt{2} + \sqrt{3} }{ \sqrt{2} + \sqrt{3} } \right \} }}$

$↦ { \bold{x = \dfrac{ \sqrt{3} - \sqrt{2} }{ (\sqrt{3} + \sqrt{2})(\sqrt{3} - \sqrt{2}) } - \left \{ \dfrac{ \sqrt{2} + \sqrt{3} }{( \sqrt{2} - \sqrt{3})( \sqrt{2} + \sqrt{3}) } \right \} }}$

$↦ { \bold{x = \dfrac{ \sqrt{3} - \sqrt{2} }{ (\sqrt{3})^{2} - ( \sqrt{2})^{2} } - \left \{ \dfrac{ \sqrt{2} + \sqrt{3} }{( \sqrt{2} )^{2} - ( \sqrt{3})^{2}} \right \} }}$

$↦{ \bold{x = \dfrac{ \sqrt{3} - \sqrt{2} }{ 3 - 2} - \left \{ \dfrac{ \sqrt{2} + \sqrt{3} }{2 - 3} \right \} }}$

$↦ { \bold{x = \dfrac{ \sqrt{3} - \sqrt{2} }{1} - \left \{ \dfrac{ \sqrt{2} + \sqrt{3} }{ - 1} \right \} }}$

$↦ { \bold{x = { \sqrt{3} - \sqrt{2} } + { \sqrt{2} + \sqrt{3} }}}$

$↦ { \bold{x = { 2\sqrt{3} }}}$

$\small{\underline{\sf{\blue{Hence-}}}}$

Value of x is = 2√3

Answer 2

Answer:

2√3 is the answer ......