Решите уравнение: $1.y {}^{3} - 6y {}^{2} = 6 - y {}^{2}$ $2.2m {}^{3} - m {}^{2} - 18m + 9 = 0$

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Question

Решите уравнение:
$1.y {}^{3} - 6y {}^{2} = 6 - y {}^{2}$
$2.2m {}^{3} - m {}^{2} - 18m + 9 = 0$

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Алгебра Eloise 2 года 2021-09-18T09:55:09+00:00 2021-09-18T09:55:09+00:00 1 Answers 0 views 0

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Captcha* 14:4+8*3-6:2*2+4:1 = ? ( )

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Jade · Answer 1 · 2021-09-18T09:56:25+00:00

В первом задании наверно опечатка , в конце не y², а просто y .

1) y³ – 6y² = 6 – y

y³ – 6y² – 6 + y= 0

(y³ – 6y²) – (6 – y) = 0

y²(y – 6) + (y – 6) = 0

(y – 6)(y² + 1) = 0

y² + 1 ≠ 0 ⇒ y – 6 = 0 y = 6

2) 2m³ – m² – 18m + 9 = 0

(2m³ – m²) – (18m – 9) = 0

m²(2m – 1) – 9(2m – 1) = 0

(2m – 1)(m² – 9) = 0

(2m – 1)(m – 3)(m + 3) = 0

или 2m – 1 = 0 и тогда m₁ = 0,5

или m – 3 = 0 и тогда m₂ = 3

или m + 3 = 0 и тогда m₃ = – 3

Ответ : 0,5 ; 3 ; – 3