Question

nationalism under root 3 + 1 upon under root 3 minus 1 equal to a + b under root 3

Answer 1

Hey


The question is :-

$\sqrt{3} + 1 \div \sqrt{3} - 1 = a + b \sqrt{3}$

$= > (\sqrt{3} + 1)( \sqrt{ 3} + 1) \div ( \sqrt{3} - 1)( \sqrt{3} + 1) = a + b \sqrt{3}$

$= > { (\sqrt{3} + 1 )}^{2} \div ( { \sqrt{3} }^{2} ) - ( {1}^{2} ) = a + b \sqrt{3}$

$= > 3 + 1 + 2 \sqrt{3} \div 3 - 1 = a + b \sqrt{3}$

$= > 4 + 2 \sqrt{3} \div 2 = a + b \sqrt{3}$

$= > 2(2 + \sqrt{3} ) \div 2 = a + b \sqrt{3}$

$= > 2 + \sqrt{3} = a + b \sqrt{3}$
By comparing both terms ,
we get
a = 2 and
$b \sqrt{3} = \sqrt{3}$
So , b = 1


thanks :)

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Answer 2

Hey fab ,

The question is :-

√3 + 1 / √3 - 1 = a + b√3

=> ( √3 + 1 )( √3 + 1 ) / ( √3 - 1 ) ( √3 + 1 ) = a + b√3
=> ( √3 + 1 ) ² / ( √3 ) ² - 1 = a + b√3
=> 3 + 1 + 2√3 / 3 - 1 = a + b√3
=> 4 + 2√3 / 2 = a + b √3
=> 2 ( 2 + √3 ) / 2 = a + b √3
=> 2 + √3 = a + b√3 .

By comparing both sides , we get ,

a = 2
and b√3 = √3
=> b = 1 .


Complicated Life :(