Вправа 655 алгебра Бевз гдз 7 клас

№ 655

а) у³ – 8y² – у + 8 = 0
у²(у – 8) – (у – 8) = 0
(у – 8)(у² – 1) = 0
(у – 8)(у – 1)(у + 1) = 0
у = 8; у = 1; у = –1;

б) х⁴ – 4х³ – 19х² + 106х – 120 = 0
х⁴ – 3х³ – х³ + 3х² – 22х² + 66х + 40х – 120 = 0
(х⁴ – 3х³) – (х³ – 3х²) – (22х² – 66х) + 40(х – 3) = 0
х³(х – 3) – х²(х – 3) – 22х(х – 3) + 40(х – 3) = 0
(х – 3)(х³ – х² – 22х + 40) = 0
(х – 3)(х³ – 4х² + 3х² – 12х – 10х + 40) = 0
(х – 3)(х²(х – 4) + 3х(х – 4) – 10(х – 4)) = 0
(х – 3)(х – 4)(х² + 3х – 10) = 0
(х – 3)(х – 4)(х² + 5х – 2х – 10) = 0
(х – 3)(х – 4)(х(х + 5) – 2(х + 5)) = 0
(х – 3)(х – 4)(х + 5)(х – 2) = 0
х – 3 = 0
х – 4 = 0
х + 5 = 0
х – 2 = 0
х = 3; х = 4; х = –5; х = 2.

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