The sum of three numbers is 14 and the sum of their squares is 100. Find the sum of cubes of those three numbers if their product is 24.radio_button_unchecked728radio_button_unchecked936radio_button_unchecked733radio_button_unchecked800

This problem can be solved using the formula for the sum of cubes, which is (a+b+c)³ = a³ + b³ + c³ + 3ab(a+b) + 3bc(a+c) + 3ca(b+c).

Given that a+b+c = 14, a²+b²+c² = 100, and abc = 24, we can substitute these values into the formula to find the sum of the cubes.

First, we need to find the value of 3ab(a+b) + 3bc(a+c) + 3ca(b+c).

This can be simplified to 3abc + 3ab² + 3bc² + 3ca².

We know that abc = 24, so 3abc = 72.

We also know that a²+b²+c² = 100, so 3ab² + 3bc² + 3ca² = 300.

Therefore, the sum of the cubes is a³ + b³ + c³ + 72 + 300 = 372 + a³ + b³ + c³.

We can find the value of a³ + b³ + c³ by subtracting 372 from the total sum of the cubes.

The sum of the cubes is therefore 372 + 24 = 396.

So, the sum of the cubes of the three numbers is 396.