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@5162
July 2022
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Найдите корни уравнения:
[tex]( x^{2} - 1)^{3} + 2( x^{2} - 1) ^{2} = 0
x^{2} (x-1)-3x(x-1)=0[/tex]
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Ртуть3
1) (x² - 1)³ + 2(x² - 1)² = 0
(x² - 1)² = 0 или x² + 1 = 0
x² - 1 = 0 x² = -1
x² = 1 ∅
x = +- 1
Ответ: x = -1
x = 1
2) x²(x - 1) - 3x(x - 1) = 0
(x - 1)(x² - 3x) = 0
x² - 3x = 0 или x - 1 = 0
x(x - 3)=0 x = 1
x = 0 x - 3 = 0
x = 3
Ответ: x = 0
x = 1
x = 3
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Answers & Comments
(x² - 1)² = 0 или x² + 1 = 0
x² - 1 = 0 x² = -1
x² = 1 ∅
x = +- 1
Ответ: x = -1
x = 1
2) x²(x - 1) - 3x(x - 1) = 0
(x - 1)(x² - 3x) = 0
x² - 3x = 0 или x - 1 = 0
x(x - 3)=0 x = 1
x = 0 x - 3 = 0
x = 3
Ответ: x = 0
x = 1
x = 3