Explanation:

Let's solve both quadratic equations and interpret the results:

- Equation I: \( 20x^2 - 17x + 3 = 0 \)

- Solve using the quadratic formula: \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).

- Here, \( a = 20 \), \( b = -17 \), and \( c = 3 \).

- Calculate discriminant: \((-17)^2 - 4 \times 20 \times 3 = 289 - 240 = 49\).

- Roots are \( x = \frac{17 \pm 7}{40} \).

- This gives \( x = \frac{24}{40} = 0.6 \) and \( x = \frac{10}{40} = 0.25 \).

- Equation II: \( 8y^2 + 10y - 3 = 0 \)

- Solve similarly using the quadratic formula: \( y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).

- Here, \( a = 8 \), \( b = 10 \), and \( c = -3 \).

- Calculate discriminant: \(10^2 - 4 \times 8 \times (-3) = 100 + 96 = 196\).

- Roots are \( y = \frac{-10 \pm 14}{16} \).

- This gives \( y = \frac{4}{16} = 0.25 \) and \( y = \frac{-24}{16} = -1.5 \).

- Comparing roots of x and y:

- \( x \) can be 0.6 or 0.25

- \( y \) can be 0.25 or -1.5

- Comparing all possibilities:

- \( 0.6 > 0.25 \)

- \( 0.6 > -1.5 \)

- \( 0.25 = 0.25 \)

- \( 0.25 > -1.5 \)

- Based on comparisons, x = y holds true in all scenarios.

Correct Answer: Option 3 - x = y