In each of the these question two equation (I) and (II) are given. You have to solve both the equtions and give answer accordingly
I `6x^2-11x+4=0`
II `3y^2-5y+2=0`

Options

A. `xgty`
B. `xgey`
C. `xley`
D. no relationship established b/w x and y

Answer

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

### Step 1: Solve Equation I: \(6x^2 - 11x + 4 = 0\)

1. **Identify the coefficients**:
- \(a = 6\), \(b = -11\), \(c = 4\)

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

3. **Calculate the discriminant**:
\[ b^2 - 4ac = (-11)^2 - 4 \cdot 6 \cdot 4 = 121 - 96 = 25 \]

4. **Substitute values into the quadratic formula**:
\[ x = \frac{-(-11) \pm \sqrt{25}}{2 \cdot 6} = \frac{11 \pm 5}{12} \]

5. **Calculate the two possible values for \(x\)**:
- First solution:
\[ x_1 = \frac{11 + 5}{12} = \frac{16}{12} = \frac{4}{3} \]
- Second solution:
\[ x_2 = \frac{11 - 5}{12} = \frac{6}{12} = \frac{1}{2} \]

### Step 2: Solve Equation II: \(3y^2 - 5y + 2 = 0\)

1. **Identify the coefficients**:
- \(a = 3\), \(b = -5\), \(c = 2\)

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

3. **Calculate the discriminant**:
\[ b^2 - 4ac = (-5)^2 - 4 \cdot 3 \cdot 2 = 25 - 24 = 1 \]

4. **Substitute values into the quadratic formula**:
\[ y = \frac{-(-5) \pm \sqrt{1}}{2 \cdot 3} = \frac{5 \pm 1}{6} \]

5. **Calculate the two possible values for \(y\)**:
- First solution:
\[ y_1 = \frac{5 + 1}{6} = \frac{6}{6} = 1 \]
- Second solution:
\[ y_2 = \frac{5 - 1}{6} = \frac{4}{6} = \frac{2}{3} \]

### Summary of Solutions:
- From Equation I: \(x = \frac{4}{3}\) or \(x = \frac{1}{2}\)
- From Equation II: \(y = 1\) or \(y = \frac{2}{3}\)

### Final Conclusion:
There is no direct relationship established between \(x\) and \(y\) based on the solutions obtained.