The value of

Question:

  1. $2+\frac{2}{5} \sqrt{30}$

  2. $2+\frac{4}{\sqrt{5}} \sqrt{30}$

  3. $4+\frac{4}{\sqrt{5}} \sqrt{30}$

  4. $5+\frac{2}{5} \sqrt{30}$


Correct Option: 1

Solution:

$y=4+\frac{1}{\left(5+\frac{1}{y}\right)}$

$y-4=\frac{y}{(5 y+1)}$

$5 y^{2}-20 y-4=0$

$\mathrm{y}=\frac{20+\sqrt{480}}{10}$

$\mathrm{y}=\frac{20-\sqrt{480}}{10} \rightarrow$ rejected

$y=2+\sqrt{\frac{480}{100}}$

Correct with Option (A)

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