Sneaky Square Roots

Algebra Level 5

Find the largest possible real value of
(x20)(yx)+(140y)(20x)+(xy)(y140),\sqrt{(x-20)(y-x)} + \sqrt{(140-y)(20-x)} + \sqrt{(x-y)(y-140)},
subject to 40x100-40\leq x \leq 100 and 20y200-20\leq y \leq 200.

Details and assumptions

Make sure you scroll to the right if necessary. You should see a comma to indicate the end of the expression.

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