Answer:
The sum of the three numbers is 36. One of the numbers is a cube number, and the other two numbers are factors of 20.
To find the cube number, we need to determine which number, when raised to the power of 3, equals a value less than or equal to 36.
Let's check:
1^3 = 1 2^3 = 8 3^3 = 27 4^3 = 64
So, the cube number must be 27.
Now let's find the factors of 20.
Factors are numbers that divide evenly into another number.
The factors of 20 are: 1, 2, 4, 5, 10, and 20 Since we need two numbers, we can choose any two of these factors that sum up to 36 - 27 = 9.
Let's try different combinations:
- 1 + 8 = 9 (both 1 and 8 are factors of 20)
- 2 + 7 = 9 (both 2 and 7 are factors of 20)
- 4 + 5 = 9 (both 4 and 5 are factors of 20)
Therefore, the three different numbers that satisfy all the given conditions are 27, 1, and 8; or 27, 2, and 7; or 27, 4, and 5.