Question

Ples answer this question

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{7 + \sqrt{5} }{7 - \sqrt{5} } = a + b \sqrt{5}$

On rationalizing the denominator we get,

$= \frac{7 + \sqrt{5} }{7 - \sqrt{5} } \times \frac{7 + \sqrt{5} }{7 + \sqrt{5} }$

Using the identity :

${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ (x + y)(x - y) = {x}^{2} - {y}^{2}$


$= \frac{ {(7)}^{2} + {( \sqrt{5} )}^{2} + 2(7)( \sqrt{5} )}{ {(7)}^{2} - {( \sqrt{5}) }^{2} } \\ \\ = \frac{49 + 5 + 14 \sqrt{5} }{49 - 5} \\ \\ = \frac{54 + 14 \sqrt{5} }{44} \\ \\ \frac{27 + 7 \sqrt{5} }{22} = a + b \sqrt{5} \\ \\ a = \frac{27}{22} \: : \: b = \frac{7}{22}$

Hope this helps!!

If you have any doubt regarding to my answer, feel free to ask in the comment section or inbox me if needed.

@Mahak24

Thanks...
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