1) x³ - 5x² + 4x > (x - 1)³
x³ - 5x² + 4x > x³ - 3x² + 3x - 1
- 5x² + 4x + 3x² - 3x + 1 > 0
- 2x² + x + 1 > 0
2x² - x - 1 < 0
D = 1 + 4*2*1 = 9
x₁ = ( 1 - 3)/4 = - 1/2
x₂ = ( 1 + 3)/ 4 = 1
+ - +
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-1/2 1 x
x∈(-1/2 ; 1)
2) x³ - 6x² + 9x > (x - 3)³
x³ - 6x² + 9x > x³ - 9x² + 27x - 27
- 6x² + 9x + 9x² - 27x + 27 > 0
3x² - 18x + 27 > 0 делим на 3
x² - 6x + 9 > 0
(x - 3)² > 0
x ∈ (- ∞; 3) ( 3; + ∞)