Maths Olympiad Prep

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Algebra Difficulty 4.9 AIME Find the answer

Five, Given: The two roots of the equation x2+85x+1=0x^{2}+85 x+1=0 are m,nm, n, and the two roots of the equation x2+96x+1=0x^{2}+96 x+1=0 are p,qp, q. Find: (m+p)⋅(n+p)⋅(m−q)⋅(n−q)(m+p) \cdot(n+p) \cdot(m-q) \cdot(n-q).

Solution

Five, Hint: Contrary to what it seems. 1791.

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