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Let M and m be the maximum and minimum values of y/x over all real pairs (x, y) satisfying (x - 3)² + (y - 3)² = 6. Find M + m.

Correct answer: 6

Solution

Tangency gives 3k² - 18k + 3 = 0 whose roots are M and m, so by Vieta's, M + m = 18/3 = 6.

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