Question

If a=(√5+2)/(√5-2) and b=(√5-2)/(√5+2) then find the value of a^2-b^2

Answer 1

hey mate ur answer is here In this picture.

Answer 2

Here's your answer !!

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It's given that,

$= > a = \frac{ \sqrt{5} + 2}{ \sqrt{5} - 2 }$

We will now rationalise it ,

$= > \frac{ \sqrt{5} + 2 }{ \sqrt{5} - 2 } \times \frac{ \sqrt{5} + 2}{ \sqrt{5} + 2}$

$= > \frac{ {( \sqrt{5} + 2) }^{2} }{( { \sqrt{5} )}^{2} - {(2)}^{2} }$

$= > \frac{5 + 4 + 4 \sqrt{5} }{1}$

$a= 9 + 4 \sqrt{5}$

Now,

$b = \frac{ \sqrt{5} - 2}{ \sqrt{5} + 2 }$

By rationalizing it,we get :-

$= > \frac{ \sqrt{5} - 2 }{ \sqrt{5} + 2 } \times \frac{ \sqrt{5} - 2}{ \sqrt{5} - 2 }$

$= > \frac{ {( \sqrt{5} - 2)}^{2} }{ {( \sqrt{5} )}^{2} - {(2)}^{2} }$

$= > \frac{5 + 4 - 4 \sqrt{5} }{1}$

$b= 9 - 4 \sqrt{5}$

We have to find value of ,

$= > {a}^{2} - {b}^{2}$

$= > {(9 + 4 \sqrt{5}) }^{2} - {(9 - 4 \sqrt{5} )}^{2}$

$= > (81 + 80 + 8 \sqrt{5} ) - (81 + 80 - 8 \sqrt{5} )$

$= > 81 + 80 + 8 \sqrt{5} - 81 - 80 + 8 \sqrt{5}$

$81 \: and \: - 81 \: 80 \: and \: - 80 \:get \: cancelled$

$= > 16 \sqrt{5}$

Hence,

$= > {a}^{2} - {b}^{2} = 16 \sqrt{5}$

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Hope it helps you!! :)

Answer 3

Here's your answer !!

____________________________

It's given that,

$= > a = \frac{ \sqrt{5} + 2}{ \sqrt{5} - 2 }$
We will now rationalise it ,
$= > \frac{ \sqrt{5} + 2 }{ \sqrt{5} - 2 } \times \frac{ \sqrt{5} + 2}{ \sqrt{5} + 2}$
$= > \frac{ {( \sqrt{5} + 2) }^{2} }{( { \sqrt{5} )}^{2} - {(2)}^{2} }$
$= > \frac{5 + 4 + 4 \sqrt{5} }{1}$
$a= 9 + 4 \sqrt{5}$

Now,
$b = \frac{ \sqrt{5} - 2}{ \sqrt{5} + 2 }$
By rationalizing it,we get :-
$= > \frac{ \sqrt{5} - 2 }{ \sqrt{5} + 2 } \times \frac{ \sqrt{5} - 2}{ \sqrt{5} - 2 }$
$= > \frac{ {( \sqrt{5} - 2)}^{2} }{ {( \sqrt{5} )}^{2} - {(2)}^{2} }$
$= > \frac{5 + 4 - 4 \sqrt{5} }{1}$
$b= 9 - 4 \sqrt{5}$
We have to find value of ,
$= > {a}^{2} - {b}^{2}$
$= > {(9 + 4 \sqrt{5}) }^{2} - {(9 - 4 \sqrt{5} )}^{2}$
$= > (81 + 80 + 8 \sqrt{5} ) - (81 + 80 - 8 \sqrt{5} )$
$= > 81 + 80 + 8 \sqrt{5} - 81 - 80 + 8 \sqrt{5}$
$81 \: and \: - 81 \: 80 \: and \: - 80 \:get \: cancelled$
$= > 16 \sqrt{5}$
Hence,
$= > {a}^{2} - {b}^{2} = 16 \sqrt{5}$
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Hope it helps you!! :)