In the following questions two equation numbered I and II are given You have to solve both equations and . . . . .
(i) `x^(3)-371=629`
(ii) `y^(3)-543=788`

Answer

To solve the given equations step by step, we will follow the same approach as described in the video transcript.

### Step 1: Solve the first equation
The first equation is:
\[ x^3 - 371 = 629 \]

**Step 1.1:** Rearrange the equation to isolate \( x^3 \):
\[ x^3 = 629 + 371 \]

**Step 1.2:** Calculate the right side:
\[ x^3 = 1000 \]

**Step 1.3:** Take the cube root of both sides:
\[ x = \sqrt[3]{1000} \]
\[ x = 10 \]

### Step 2: Solve the second equation
The second equation is:
\[ y^3 - 543 = 788 \]

**Step 2.1:** Rearrange the equation to isolate \( y^3 \):
\[ y^3 = 788 + 543 \]

**Step 2.2:** Calculate the right side:
\[ y^3 = 1331 \]

**Step 2.3:** Take the cube root of both sides:
\[ y = \sqrt[3]{1331} \]
\[ y = 11 \]

### Step 3: Summary of results
We have found the values:
- \( x = 10 \)
- \( y = 11 \)

### Step 4: Compare the values
Now we can compare \( x \) and \( y \):
Since \( y = 11 \) and \( x = 10 \), we can conclude that:
\[ y > x \]

### Final Answer
- \( x = 10 \)
- \( y = 11 \)

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