Find the value of a :
frac{3-sqrt{5}}{3+2 sq | vedclass

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Question

(NONE) To solve the expression,we rationalize the denominator:
$L.H.S. = \frac{3-\sqrt{5}}{3+2 \sqrt{5}} 	imes \frac{3-2 \sqrt{5}}{3-2 \sqrt{5}}$
$

Vedclass · Accepted Answer

$\frac{9}{11}$

Vedclass · Answer

(NONE) To solve the expression,we rationalize the denominator:
$L.H.S. = \frac{3-\sqrt{5}}{3+2 \sqrt{5}} 	imes \frac{3-2 \sqrt{5}}{3-2 \sqrt{5}}$
$= \frac{9 - 6\sqrt{5} - 3\sqrt{5} + 2(5)}{3^2 - (2\sqrt{5})^2}$
$= \frac{9 - 9\sqrt{5} + 10}{9 - 20} = \frac{19 - 9\sqrt{5}}{-11}$
$= -\frac{19}{11} + \frac{9}{11}\sqrt{5}$
Comparing this with $a\sqrt{5} - \frac{19}{11}$,we get:
$a\sqrt{5} - \frac{19}{11} = \frac{9}{11}\sqrt{5} - \frac{19}{11}$
Therefore,$a = \frac{9}{11}$.

Find the value of $a$ :
$\frac{3-\sqrt{5}}{3+2 \sqrt{5}}=a \sqrt{5}-\frac{19}{11}$

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Find the value of $a$ : $\frac{3-\sqrt{5}}{3+2 \sqrt{5}}=a \sqrt{5}-\frac{19}{11}$