Question

7+√5/7-2√5=

Solve this...

Answer 1

Heya there !!!
Here is the answer you were looking for:

Using the identity:

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

$\frac{7 + \sqrt{5} }{7 - 2 \sqrt{5} }$

On rationalizing the denominator we get,

$= \frac{7 + \sqrt{5} }{7 - 2 \sqrt{5} } \times \frac{7 + 2 \sqrt{5} }{7 + 2 \sqrt{5} } \\ \\ = \frac{7(7 + 2 \sqrt{5} ) + \sqrt{5}(7 + 2 \sqrt{5} )}{ {(7)}^{2} - {(2 \sqrt{5}) }^{2} } \\ \\ = \frac{49 + 14 \sqrt{5} + 7 \sqrt{5} + 10 }{49 - 20} \\ \\ = \frac{59 + 21 \sqrt{5} }{29}$

Hope this helps!!!

If you have any doubt regarding to my answer, please ask in the comment section ^_^

@Mahak24

Thanks...
☺☺

Answer 2

heya!!!!


(7+√5)/(7-2√5)

Multiplying and dividing with 7+2√5, we get

(7+√5)(7+2√5)/(7-2√5)(7+2√5)

(49+14√5+7√5+10)/(49-20)

(59+21√5)/29

I hope this will help u ;)