Can this will go to Level 2?

$\begin{aligned} y + \frac{1}{y} & = 3 \\ \Rightarrow \left(y + \frac{1}{y}\right)^2 & = 9 \\ y^2 + 2 + \frac{1}{y^2} & = 9 \\ \Rightarrow y^2 + \frac{1}{y^2} & = 7 \\ \left(y + \frac{1}{y}\right)\left(y^2 + \frac{1}{y^2}\right) & = 3 \times 7 \\ y^3 + y + \frac{1}{y} + \frac{1}{y^3} & = 21 \\ \Rightarrow y^3 + \frac{1}{y^3} & = 21 - 3 = 18 \\ \left(y^2 + \frac{1}{y^2}\right)\left(y^3 + \frac{1}{y^3}\right) & = 7 \times 18 \\ y^5 + y + \frac{1}{y} + \frac{1}{y^5} & = 126 \\ \Rightarrow y^5 + \frac{1}{y^5} & = 126 - 3 = \boxed{123} \end{aligned}$

we could find the answer by just looking at the options i.e. the answer must be less than $3^{5}$ =243 So this eliminates the first two options but the answer is certainly not as less as 0 or 1 therefore it leaves us only with one option(viz the answer) $\boxed{123}$

(y + 1/y)^3 = 3^3 = 27

y^3 + 1/y^3 + 3y + 3/y = 27

y^3 +1/y^3 = 27 - 3(y + 1/y) = 27 - 9 = 18

(y + 1/y)^5 = y^5 + 1/y^5 + 5(y^3 + 1/y^3) + 10(y + 1/y) = 3^5 = 243

y^5 + 1/y^5 = 243 - 5(y^3 + 1/y^3) - 10(y + 1/y)

y^5 + 1/y^5 = 243 - 5(18) - 10(3) = 123

y^5 + 1/y^5 =123