Two equations (I) and (II) are given in each question. On the basis of these equations you have to decide the relation between x and y and give answer
I. `(18)/(x^(2)) + (6)/( x) - (12)/( x^(2)) = (8)/( x^(2))`
II. ` y^(3) + 9 . 68 + 5 . 64 = 16. 95 `

Options

A. If ` x gt y `
B. If ` x lt y `
C. If ` x ge Y`
D. If ` x le y `

Answer

To solve the given equations and determine the relationship between \( x \) and \( y \), we will follow these steps:

### Step 1: Solve the first equation for \( x \)

Given the first equation:
\[ \frac{18}{x^2} + \frac{6}{x} - \frac{12}{x^2} = \frac{8}{x^2} \]

Combine the terms on the left side:
\[ \frac{18 - 12}{x^2} + \frac{6}{x} = \frac{8}{x^2} \]
This simplifies to:
\[ \frac{6}{x^2} + \frac{6}{x} = \frac{8}{x^2} \]

Next, we can eliminate the \( \frac{1}{x^2} \) term by multiplying the entire equation by \( x^2 \) (assuming \( x \neq 0 \)):
\[ 6 + 6x = 8 \]

Rearranging gives:
\[ 6x = 8 - 6 \]
\[ 6x = 2 \]
\[ x = \frac{2}{6} = \frac{1}{3} \]

### Step 2: Solve the second equation for \( y \)

Given the second equation:
\[ y^3 + 9.68 + 5.64 = 16.95 \]

Combine the constants on the left side:
\[ y^3 + (9.68 + 5.64) = 16.95 \]
Calculating the sum:
\[ y^3 + 15.32 = 16.95 \]

Now, isolate \( y^3 \):
\[ y^3 = 16.95 - 15.32 \]
\[ y^3 = 1.63 \]

Taking the cube root gives:
\[ y = \sqrt[3]{1.63} \approx 1.176 \]

### Step 3: Compare \( x \) and \( y \)

Now we have:
\[ x = \frac{1}{3} \quad \text{and} \quad y \approx 1.176 \]

Since \( \frac{1}{3} \approx 0.333 < 1.176 \), we conclude that:
\[ y > x \]

### Final Conclusion

Thus, the relationship between \( x \) and \( y \) is:
\[ y > x \]

---