Consider the set

MATHEMATICS · Single correct · AoPS · Mathematics · More Variables · More Variables

Problem

Consider the set S={(a,b,c)/a2−1=bc and b2−1=ac and a,b,c∈Z}S = \{ (a, b, c) / a^2 - 1 = bc \text{ and } b^2 - 1 = ac \text{ and } a, b, c \in \mathbb{Z} \}, then which of the following are correct? (A) The value of ∑(a,b,c)∈S(a2+b2+c2)\sum_{(a,b,c) \in S} (a^2 + b^2 + c^2) is 8. (B) Cardinal number of SS is 8. (C) Number of elements in SS such that a<ba < b are 3. (D) The equation whose roots are (a+b)≠0(a+b) \neq 0 is x6−6x4+9x2−4=0x^6 - 6x^4 + 9x^2 - 4 = 0.

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