1.

Find the value of a if 3-root5/3+2root5=aroot5-19/11

Answer» HI...☺

Here is your ANSWER...✌

GIVEN THAT,

\frac{3 - \sqrt{5} }{ 3 + 2 \sqrt{5} } = \frac{a \sqrt{5} - 19}{11} \: \: \: \: \: \: \: \: \: \: .....(<klux>1</klux>) \\
On RATIONALISING LHS
We GET,

LHS

= \frac{3 - \sqrt{5} }{3 + 2 \sqrt{5} } \times \frac{3 - 2 \sqrt{5} }{3 - 2 \sqrt{5} } \\ \\ = \frac{9 - 6 \sqrt{5} - 3 \sqrt{5} + 10}{ {3}^{2} - {(2 \sqrt{5} )}^{2} } \\ \\ = \frac{19 - 9 \sqrt{5} }{9 - 20} \\ \\ = \frac{19 - 9 \sqrt{5} }{ - 11} \\ \\ = \frac{9 \sqrt{5} - 19}{11}

Now

From (1) we have,

\frac{9 \sqrt{5} - 19}{11} = \frac{a \sqrt{5} - 19}{11} \\ \\ \implies a = 9


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