Question

please answer this question​

Answer 1

Solution :-

$\purple\longmapsto\footnotesize \: y = 2 + \frac{1}{4 + \frac{1}{4 + \frac{1}{4 + .............. \infty} } } \\ \\ \bf \: Adding\:2\:Both\:Sides, \\ \\ \purple\longmapsto\footnotesize \: y + 2 = 2 + 2 + \frac{1}{4 + \frac{1}{4 + \frac{1}{4 + .............. \infty} } } \\ \\ \purple\longmapsto\footnotesize \: y + 2 = 4 + \frac{1}{4 + \frac{1}{4 + \frac{1}{4 + .............. \infty} } } \\ \\ \purple\longmapsto\footnotesize \: y + 2 = 4 +\frac{1}{(y + 2)}\\\\\purple\longmapsto\footnotesize \: y + 2 = \frac{4(y + 2) + 1}{(y + 2)} \\ \\ \purple\longmapsto\footnotesize \: (y + 2)^{2} = 4y + 8 + 1 \\ \\ \purple\longmapsto\footnotesize \: {y}^{2} + \cancel{4y} + 4 = \cancel{4y} + 9 \\ \\ \purple\longmapsto\footnotesize \: y^{2} = 9 - 4 \\ \\ \purple\longmapsto\footnotesize \: {y}^{2} = 5 \\ \\ \purple\longmapsto\footnotesize\: \red\therefore\:\boxed{\pink{y=\pm \sqrt{5}}}$