If the roots of the equation `(c^2-a b)x^2-2(a^2-b c)x+b^2-a c=0` are equal, prove that either `a=0` or `a^3+b^3+c^3=3a b cdot`

Explanation

To prove that either \( a = 0 \) or \( a^3 + b^3 + c^3 = 3abc \) when the roots of the quadratic equation

\[ (c^2 - ab)x^2 - 2(a^2 - bc)x + (b^2 - ac) = 0 \]

are equal, we will analyze the discriminant of the quadratic equation.

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