1. **State the problems:** We have two problems: (1) Solve the quadratic equation $$6y^2 - 15y + 1 = 0$$. (2) Simplify the expression $$4y^2 + \frac{1}{4y^2}$$. 2. **Solve the quadratic equation:** The quadratic equation is $$6y^2 - 15y + 1 = 0$$. Use the quadratic formula: $$y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $$a=6$$, $$b=-15$$, and $$c=1$$. Calculate the discriminant: $$\Delta = b^2 - 4ac = (-15)^2 - 4 \times 6 \times 1 = 225 - 24 = 201$$. Calculate the roots: $$y = \frac{15 \pm \sqrt{201}}{12}$$. 3. **Simplify the expression:** Given: $$4y^2 + \frac{1}{4y^2}$$ This expression cannot be simplified further without knowing the value of $$y$$, so the simplified form is: $$4y^2 + \frac{1}{4y^2}$$. **Final answers:** (1) $$y = \frac{15 \pm \sqrt{201}}{12}$$ (2) $$4y^2 + \frac{1}{4y^2}$$