Can you show me?... i got stuck too. XDNEILS BOHR said:got the ans finally using AM GM only...
The expression (a^3 + b^3 + c^3 - 3abc) represents the sum of cubes of three distinct integers a, b, and c, minus three times their product. This expression is commonly known as the "cubed polynomial."
By finding the minimum value of this expression, we can determine the smallest possible result when adding the cubes of three distinct integers and subtracting three times their product. This can be useful in various mathematical and scientific applications.
The min value of this expression can be calculated by finding the roots of the derivative of the expression, setting it equal to zero, and solving for a, b, and c. This will result in the minimum value of the expression.
Yes, this expression can have a negative min value. This occurs when the three distinct integers a, b, and c are negative. In this case, the minimum value would be equal to the negative value of the expression.
This expression has various real-world applications, such as in physics, where it can be used to calculate the minimum energy state of a system. It is also commonly used in optimization problems in mathematics and computer science.