求 a 所有 可能值之積

17x⁴ + 34ax³ + (25a²+10)x² + (8a³ +10a)x + (a⁴+25) = 0
(16x⁴ + 32ax³ + 24a²x² + 8a³x + a⁴) + (x⁴+ 2ax³ + (a²+10)x² + 10ax + 25) = 0
(2x + a)⁴+ (x⁴ + 2ax³ + 10x² + a²x² + 10ax + 25) = 0
(2x + a)⁴+ (x⁴ + 2x² (ax + 5) + (ax + 5)²) = 0
(2x + a)⁴+ (x² + ax + 5)² = 0
⇒
2x + a = 0 and x² + ax + 5 = 0 x = - a/2 , sub. into x² + ax + 5 = 0 :a²/4 - a²/2 + 5 = 0
a² = 20∴ The product of all possible values of a = - 20.

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雨後晴空 知識長
真的是太強了!!