1) (3x + 12)(x² - 2x) < 0
3 * (x + 4) * x * (x - 2) < 0 |: 3
x(x + 4)(x - 2) < 0
- + - +
______₀_____₀______₀______
- 4 0 2
////////////// //////////////
Ответ : x ∈ ( - ∞ ; - 4) ∪ (0 ; 2)
2) (x² - 25)(x² - 9) < 0
(x - 5)(x + 5)(x - 3)(x + 3) < 0
+ - + - +
_____₀_____₀____₀____₀_____
- 5 - 3 3 5
////////// //////////
Ответ : x ∈ (- 5 ; - 3) ∪ (3 ; 5)
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Verified answer
1) (3x + 12)(x² - 2x) < 0
3 * (x + 4) * x * (x - 2) < 0 |: 3
x(x + 4)(x - 2) < 0
- + - +
______₀_____₀______₀______
- 4 0 2
////////////// //////////////
Ответ : x ∈ ( - ∞ ; - 4) ∪ (0 ; 2)
2) (x² - 25)(x² - 9) < 0
(x - 5)(x + 5)(x - 3)(x + 3) < 0
+ - + - +
_____₀_____₀____₀____₀_____
- 5 - 3 3 5
////////// //////////
Ответ : x ∈ (- 5 ; - 3) ∪ (3 ; 5)