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

`D=4(a^(2)-bc)^(2)-4(c^(2)-ab)(b^(2)-ac)`
Now, `D=0implies(a^(2)-bc)^(2)-(c^(2)-ab)(b^(2)-ac)=0`
`impliesa^(4)-3a^(2)bc+ac^(3)+ab^(3)=0`
`impliesa(a^(3)+b^(3)+c^(3)-2abc)=0`
`impliesa=0" or "a^(3)+b^(3)+c^(3)=3abc.`