(x-2)do trzeciej potegi +10x do drugiej potegi >badz rowne (x-2)(x+3)do drugiej potegi
(x-2)^3 + 10x^2 >= (x-2)(x+3)^2
x^3 - 6x^2 + 12x - 8 >= (x-2)(x^2 + 6x + 9)
x^3 - 6x^2 + 12x - 8 >= x^3 + 6x^2 + 9x - 2x^2 - 12x -18
12x - 8 >= -3x -18
15x >= -10
x >= = 2/3
(x - 2)³ + 10x² ≥ (x - 2)(x + 3)²
x³ - 8 + 10x² ≥ (x² + 3x - 2x - 6)²
x³ - 8 + 10x² ≥ x³ + 9x² - 4x² - 36
x³ - x³ + 10x² - 9x² + 4x² ≥ -36 + 8
5x² ≥ -28
5x ≥ √28 (dzielimy obustronnie przez 5)
x ≥ √28 : 5
x ≥ √4 × 7 : 5
x ≥ 2√7 : 5
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(x-2)^3 + 10x^2 >= (x-2)(x+3)^2
x^3 - 6x^2 + 12x - 8 >= (x-2)(x^2 + 6x + 9)
x^3 - 6x^2 + 12x - 8 >= x^3 + 6x^2 + 9x - 2x^2 - 12x -18
12x - 8 >= -3x -18
15x >= -10
x >= = 2/3
(x - 2)³ + 10x² ≥ (x - 2)(x + 3)²
x³ - 8 + 10x² ≥ (x² + 3x - 2x - 6)²
x³ - 8 + 10x² ≥ x³ + 9x² - 4x² - 36
x³ - x³ + 10x² - 9x² + 4x² ≥ -36 + 8
5x² ≥ -28
5x ≥ √28 (dzielimy obustronnie przez 5)
x ≥ √28 : 5
x ≥ √4 × 7 : 5
x ≥ 2√7 : 5