Find the value of a :

frac{3-sqrt{5}}{3+2 | vedclass

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Question

$L.H.S. =\frac{3-\sqrt{5}}{3+2 \sqrt{5}}=\frac{3-\sqrt{5}}{3+2 \sqrt{5}} 	imes \frac{3-2 \sqrt{5}}{3-2 \sqrt{5}}$

$=\frac{(3-\sqrt{5})(3-2 \sqrt{5

Vedclass · Accepted Answer

$\frac{19}{11}$

Vedclass · Answer

$L.H.S. =\frac{3-\sqrt{5}}{3+2 \sqrt{5}}=\frac{3-\sqrt{5}}{3+2 \sqrt{5}} 	imes \frac{3-2 \sqrt{5}}{3-2 \sqrt{5}}$

$=\frac{(3-\sqrt{5})(3-2 \sqrt{5})}{(3)^{2}(2 \sqrt{5})^{2}}$

$=\frac{9-6 \sqrt{5}-3 \sqrt{5}+10}{9-20}=\frac{19-9 \sqrt{5}}{-11}$

Now, $\frac{19-9 \sqrt{5}}{-11}=a \sqrt{5}-\frac{19}{11}$

$\Rightarrow \frac{-19}{11}+\frac{9}{11} \sqrt{5}=a \sqrt{5}-\frac{19}{11}$

$\Rightarrow \frac{9}{11} \sqrt{5}-\frac{19}{11}=a \sqrt{5}-\frac{19}{11}$

Hence, $a=\frac{19}{11}$

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