Math, asked by ny184480, 1 year ago

(2/√5+√3)+(1/√6-√3)+(1/√6+√5)

Answers

Answered by Soumil2005

Pls check the answer to your question.

Attachments:

ny184480: No sir.... The answer is 2√6

Soumil2005: Pls check your question

Soumil2005: If the answer is coming to be 2√6 then the question should be

Soumil2005: 2/√5+√3 + 3/√6-√3 + 1/√6+√5

Soumil2005: In the second part that is 1/√6-√3 there should be 3 instead of 1

Soumil2005: It should be a printing mistake

ny184480: Yes... Question is misprinted.... They forget 3 in middle term....

Answered by chopraneetu

$\frac{2}{ \sqrt{5} + \sqrt{3} } + \frac{1}{ \sqrt{6 } - \sqrt{3}} + \frac{1}{ \sqrt{6 } + \sqrt{5} } \\ = \frac{2}{ \sqrt{5} + \sqrt{3} } \times \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} - \sqrt{3} } + \frac{1}{ \sqrt{6 } - \sqrt{3}} \times \frac{ \sqrt{6} + \sqrt{3} }{ \sqrt{6} + \sqrt{3} } + \frac{1}{ \sqrt{6 } + \sqrt{5} } \times \frac{ \sqrt{6} - \sqrt{5} }{ \sqrt{6} - \sqrt{5} } \\ = \frac{2( \sqrt{5} - \sqrt{3})}{ { \sqrt{5} }^{2} - { \sqrt{3} }^{2} } + \frac{ \sqrt{6} + \sqrt{3} }{ { \sqrt{6} }^{2} - { \sqrt{3} }^{2} } + \frac{ \sqrt{6} - \sqrt{5} }{ { \sqrt{6} }^{2} - { \sqrt{5} }^{2} } \\ = \sqrt{5} - \sqrt{3} +\frac{ \sqrt{6} + \sqrt{3} }{3} + \sqrt{6} - \sqrt{5} \\ = \frac{4 \sqrt{6 } - 2 \sqrt{3} }{3}$

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