Question

root5-2/root5+2 - root5+2/root5-2

Answer 1

$\huge \bf {HEY \: FRIENDS!!}$


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$\huge \bf \underline{Here \: is \: your \: answer↓}$


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$\huge \boxed{Rationalise:-)}$

$\bf = \frac{ \sqrt{5} - 2 }{ \sqrt{5} + 2 } - \frac{ \sqrt{5} + 2 }{ \sqrt{5} - 2} .$

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


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

▶⏩ Using identity:-)
$\huge \boxed{ {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab.}$
$\huge \boxed{ {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab.}$


$\bf =( \frac{25 + 4 - 4 \sqrt{5} }{5 - 4} ) -( \frac{25 + 4 +4 \sqrt{5} }{5 - 4} ).$


$\bf = (25 + 4 - 4 \sqrt{5} ) - (25 + 4 + 4 \sqrt{5} ).$


$\bf = 25 + 4 - 4 \sqrt{5} - 25 - 4 - 4 \sqrt{5} .$


$\huge \bf = - 8 \sqrt{5} .$


✅✅ Hence, it is rationalised ✔✔.



$\huge \boxed{THANKS}$


$\huge \bf \underline{Hope \: it \: is \: helpful \: for \: you}$

Answer 2

Step-by-step explanation:

This is the step by step method to get the answer, the person who had earlier posted the answer got the correct answer but has got a glitch in the end because root 5^2 is not 25, it's 5..... so I thought that I would rather send the accurate method. Pls mark my answer as the BRAINLIEST