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suppose `x_1,` and `x_2` are the point of maximum and the point of minimum respectively of the function `f(x)=2x^3-9ax^2 + 12a^2x + 1` respectively, `(a> o)` then for the equality `x_1^2 = x_2` to be true the value of `'a'` must be

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Let x_(1) and x_(2) are the points of maximum and minimum of function f(x)=2x^(3)-9ax^(2)+12a^(2)x+1 respectively, (a>0).If x_(1)^(3)=8x_(2) then the sum of all possible values of 'a' is

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