Suppose a and b are positive integers satisfying 1≤a≤31, 1≤b≤31 such that the polynomial P(x)=x3−ax2+a2b3x+9a2b2 has roots r, s, and t.

Question

Given that there exists a positive integer k such that (r+s)(s+t)(r+t)=k2, compute the maximum possible value of ab.

Answer 1

34

Answer 2

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Answer 3

775