IMO 1972 LL BUL2

Find all real values of the parameter a for which the system of

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IMO 1972 LL BUL2

Origin: BUL

Problem

Find all real values of the parameter a for which the system of equations x4 = yz −x2 + a, y4 = zx −y2 + a, z4 = xy −z2 + a, has at most one real solution.