Three numbers are in the ratio 1 : 2 : 3 : The sum of their cubes is 98784. Find the numbers.

Explanation

To solve the problem step by step, we will follow the instructions given in the video transcript and break it down clearly.

### Step-by-Step Solution:

1. **Define the Variables**:
Let the three numbers be represented as \( k \), \( 2k \), and \( 3k \) based on the ratio 1:2:3.

2. **Set Up the Equation**:
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