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Problem No. 50

Algebra Level 5

Find the maximum value of the expression \[ \sqrt{(x-4)^2 + (x^3 - 2)^2 } - \sqrt{ (x-2)^2 + (x^3 + 4)^2} \] as \(x\) runs through all real numbers.

\[3\sqrt{10}\] \[4\sqrt{10}\] \[5\sqrt{10}\] \[2\sqrt{10}\]

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by Benedict Dimacutac

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