In each of these questions two equations numbered I and n are given. You have to solve both the equations and give answer
I. `2x^2-17x+35=0`
II. `3y^2-10y+7=0`

Options

A. `xley`
B. `xgty`
C. `xgey`
D. the relationship can’t be established

Answer

To solve the given equations step by step, we will first tackle each quadratic equation separately.

### Step 1: Solve the first equation \(2x^2 - 17x + 35 = 0\)

1. **Identify the coefficients**:
- \(a = 2\), \(b = -17\), \(c = 35\)

2. **Use the quadratic formula**:
The quadratic formula is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

3. **Calculate the discriminant**:
\[ b^2 - 4ac = (-17)^2 - 4 \cdot 2 \cdot 35 = 289 - 280 = 9 \]

4. **Substitute the values into the quadratic formula**:
\[ x = \frac{-(-17) \pm \sqrt{9}}{2 \cdot 2} = \frac{17 \pm 3}{4} \]

5. **Calculate the two possible values for \(x\)**:
- \(x_1 = \frac{17 + 3}{4} = \frac{20}{4} = 5\)
- \(x_2 = \frac{17 - 3}{4} = \frac{14}{4} = 3.5\)

### Step 2: Solve the second equation \(3y^2 - 10y + 7 = 0\)

1. **Identify the coefficients**:
- \(a = 3\), \(b = -10\), \(c = 7\)

2. **Use the quadratic formula**:
\[ y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

3. **Calculate the discriminant**:
\[ b^2 - 4ac = (-10)^2 - 4 \cdot 3 \cdot 7 = 100 - 84 = 16 \]

4. **Substitute the values into the quadratic formula**:
\[ y = \frac{-(-10) \pm \sqrt{16}}{2 \cdot 3} = \frac{10 \pm 4}{6} \]

5. **Calculate the two possible values for \(y\)**:
- \(y_1 = \frac{10 + 4}{6} = \frac{14}{6} = \frac{7}{3} \approx 2.33\)
- \(y_2 = \frac{10 - 4}{6} = \frac{6}{6} = 1\)

### Summary of Solutions:
- The solutions for \(x\) are \(5\) and \(3.5\).
- The solutions for \(y\) are \(2.33\) and \(1\).

### Final Comparison:
- The values of \(x\) are \(5\) and \(3.5\).
- The values of \(y\) are \(2.33\) and \(1\).
- The largest value of \(x\) (which is \(5\)) is greater than the largest value of \(y\) (which is \(2.33\)).

### Conclusion:
Since \(x\) is greater than \(y\), the answer is \(x > y\).