Question

$\frac{6 + 2 \sqrt{11} }{5 - 3 \sqrt{11} }$

Answer 1

Heya!!! User!!! ✌

Here's your answer friend,

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==> (6 + 2√11)/(5 - 3√11)

Thus,

➡ Rationalising the denominator

we have,

===> 6 + 2√11 /5 - 3√11

==> 6 + 2√11 / 5 - 3√11 X 5 + 3√11 / 5 + 3√11

==> (6 + 2√11)(5 + 3√11) / (5 - 3√11)(5 + 3√11)

==> 30 + 18√11 + 10√11 + 66 / (5)² - (3√11)²

..................{ Since, (a + b) (a - b) = (a) ² - (b)² }

==> 96 + 28√11 / 25 - 99

==> 96 + 28√11 / -(74)

==> Since, denominator cannot be negative,

Hence,

the required answer is

➡-(96 + 28√11)/74

➡-96 - 28√11 / 74

==> 2/2 X (-48 - 14√11)/(37) ............{ on taking 2 common outside }

==> (-48 - 14√11) / 37

Is the final answer.

HOPE YOU GOT YOUR ANSWER :)

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