Problem No. 50

Algebra Level 5

Find the maximum value of the expression (x4)2+(x32)2(x2)2+(x3+4)2 \sqrt{(x-4)^2 + (x^3 - 2)^2 } - \sqrt{ (x-2)^2 + (x^3 + 4)^2} as xx runs through all real numbers.

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