In each of questions two eqautions numbered Iand II are given you have to solve both equations and give answer
I.`2x^2-13x+21=0`
II.`3y^2-14y+15=0`

Options

A. If `xlty`
B. `if xley`
C. if `xgty`
D. `if xgey`

Answer

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

### Step 1: Solve the first equation \(2x^2 - 13x + 21 = 0\)

1. **Identify the coefficients**:
- \(a = 2\), \(b = -13\), \(c = 21\)

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

3. **Calculate the discriminant**:
\[ b^2 - 4ac = (-13)^2 - 4 \cdot 2 \cdot 21 = 169 - 168 = 1 \]

4. **Substitute values into the quadratic formula**:
\[ x = \frac{-(-13) \pm \sqrt{1}}{2 \cdot 2} = \frac{13 \pm 1}{4} \]

5. **Calculate the two possible values for \(x\)**:
- First value:
\[ x_1 = \frac{13 + 1}{4} = \frac{14}{4} = 3.5 \]
- Second value:
\[ x_2 = \frac{13 - 1}{4} = \frac{12}{4} = 3 \]

### Step 2: Solve the second equation \(3y^2 - 14y + 15 = 0\)

1. **Identify the coefficients**:
- \(a = 3\), \(b = -14\), \(c = 15\)

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

3. **Calculate the discriminant**:
\[ b^2 - 4ac = (-14)^2 - 4 \cdot 3 \cdot 15 = 196 - 180 = 16 \]

4. **Substitute values into the quadratic formula**:
\[ y = \frac{-(-14) \pm \sqrt{16}}{2 \cdot 3} = \frac{14 \pm 4}{6} \]

5. **Calculate the two possible values for \(y\)**:
- First value:
\[ y_1 = \frac{14 + 4}{6} = \frac{18}{6} = 3 \]
- Second value:
\[ y_2 = \frac{14 - 4}{6} = \frac{10}{6} = \frac{5}{3} \approx 1.67 \]

### Step 3: Compare the values of \(x\) and \(y\)

We have the following values:
- \(x_1 = 3.5\), \(x_2 = 3\)
- \(y_1 = 3\), \(y_2 = \frac{5}{3} \approx 1.67\)

Now we can compare:
1. \(x_1 = 3.5\) and \(y_2 \approx 1.67\): \(x_1 > y_2\)
2. \(x_2 = 3\) and \(y_1 = 3\): \(x_2 = y_1\)
3. \(x_1 = 3.5\) and \(y_1 = 3\): \(x_1 > y_1\)

### Conclusion

From the comparisons, we can conclude that \(x\) is greater than or equal to \(y\).

### Final Answer
The relation between \(x\) and \(y\) is \(x \geq y\).

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