Verified answer

5x³ -  3x² - 3x + 5 = 0

5x³ +5 -  3x² - 3x  = 5(x³ + 1) - 3x(x + 1) = 5(x + 1)(x² - x + 1) -3x(x + 1) = (x + 1)(5x² -5x + 5 - 3x) = (x + 1)(5x² - 8x + 5) = 0

x = -1

5x² - 8x + 5 = 0

D = 64 - 80 < 0

x ∈ ∅ при x ∈ R

ответ -1

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(x + 1/x)² - 5(x + 1/x) + 6 = 0

x ≠ 0

x + 1/x = t

t² - 5t + 6 = 0

D = 25 - 24 = 1

t12 = (5 +- 1)/2 = 2   3

1. t = 2

x + 1/x = 2

(x² - 2x + 1)/x = 0

(x - 1)²/ x = 0

x = 1

2. t = 3

x + 1/x = 3

(x² - 3x + 1)/x = 0

D = 9 - 4 = 5

x12 = (3 +- √5)/2

ответ (3 +- √5)/2, 1

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x⁴ - 5x³ + 8x² - 5x + 1 = 0

x ≠ 0

разделим на x²

1/x² + x² = 1/x² + 2*x²*1/x² + x² - 2*x²*1/x² = (x + 1/x)² - 2

x² - 5x + 8 - 5/x + 1/x² = x² + 1/x² - 5(x + 1/x) + 8 = (x + 1/x)² - 2 - 5(x + 1/x) + 8 = (x + 1/x)² - 5(x + 1/x) + 6 = 0

x + 1/x = t

t² - 5t + 6 = 0

это уравнение было номер 2

D = 25 - 24 = 1

t12 = (5 +- 1)/2 = 2   3

1. t = 2

x + 1/x = 2

(x² - 2x + 1)/x = 0

(x - 1)²/ x = 0

x = 1

2. t = 3

x + 1/x = 3

(x² - 3x + 1)/x = 0

D = 9 - 4 = 5

x12 = (3 +- √5)/2

ответ (3 +- √5)/2, 1

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