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Consider the conic ex^2 + y^2 2e^2x 2^2y + e^3 + 3 = e. Suppose P is any point on the conic and S1, S2 are the foci of the conic, then the maximum value of (PS1 + PS2) is

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Let a, b, c, d be numbers in the set {1, 2, 3, 4, 5, 6} such that the curves y = 2x^3 + ax + b and y = 2x^3 + cx + d have no point in common. The maximum possible value of (a - c)^2 + b d is The value of tan81° – tan63° – tan27° + tan9° is