1) (x + 2)(x² - 2x + 4) - x(x - 3)(x + 3) - 42 =
х³ - 2х + 4х + 2х² - 4х + 8 - х³ - 3х² + 3х² + 9х - 42 =
х³ - х³ + 2х² - 3х² + 3х² - 2х + 4х - 4х + 9х + 8 - 42 =
2х² + 7х - 34
2) (x - 3)(x² + 3x + 9) - x(x²- 16) + 21=
х³ + 3х² + 9х - 3х² - 9х - 27 - х³ + 16х + 21 =
х³ - х³ + 3х² - 3х² + 9х - 9х + 16х - 27 + 21 =
16х - 6
3) (2x - 1)(4x² + 2x + 1)-23 - 4x(2x² + 3) =
8х³ + 4х² + 2х - 4х² - 2х - 1 - 23 - 8х³ - 12х =
8х³ - 8х³ + 4х² - 4х² + 2х - 2х - 12х - 1 - 23 =
-12х - 24
4) 16x(4x² - 5) + 17 - (4x + 1)(16x² - 4x + 1) =
64х³ - 80х + 17 - 64х³ - (16х + 4х + 16х² - 4х + 1) =
64х³ - 80х + 17 - 64х³ - 16х - 4х - 16х² + 4х - 1 =
64х³ - 64х³ - 16х² - 80х - 16х - 4х + 4х + 17 - 1 =
- 16х² - 96х + 16
+ _ +
_________________________
-1/3 3
На (-≈;1/3) и (3;≈) модуль молож, а (-1/3;3) отриц
1)x<-1/3
(3x+1)/(x-1)<3
(3x+1-3x+9)/(x-1)<0
10/x-1<0
_ +
______________
1
x<1 ,но x<-1/3⇒x∈(-≈;-1/3)
2)-1/3≤x≤3
(3x+1)/(x-1)>-3
(3x+1+3x-9)/(x-1)>0
(6x-8)/(x-1)>0
+ _ +
__________________________________
1 4/3
x<1 и x>4/3 ,но -1/3≤x≤3⇒x∈[-/3;1) U (4/3;3]
3)x>3
(3x+1)/(x-1)<3
(3x+1-3x+9)/(x-1)<0
10/x-1<0
_ +
______________
1
x<1 ,но x>3 нет решения
ответ x∈[-/3;1) U (4/3;3] и x∈(-≈;-1/3)⇒х∈(-≈;1) U (4/3;3]
1) (x + 2)(x² - 2x + 4) - x(x - 3)(x + 3) - 42 =
х³ - 2х + 4х + 2х² - 4х + 8 - х³ - 3х² + 3х² + 9х - 42 =
х³ - х³ + 2х² - 3х² + 3х² - 2х + 4х - 4х + 9х + 8 - 42 =
2х² + 7х - 34
2) (x - 3)(x² + 3x + 9) - x(x²- 16) + 21=
х³ + 3х² + 9х - 3х² - 9х - 27 - х³ + 16х + 21 =
х³ - х³ + 3х² - 3х² + 9х - 9х + 16х - 27 + 21 =
16х - 6
3) (2x - 1)(4x² + 2x + 1)-23 - 4x(2x² + 3) =
8х³ + 4х² + 2х - 4х² - 2х - 1 - 23 - 8х³ - 12х =
8х³ - 8х³ + 4х² - 4х² + 2х - 2х - 12х - 1 - 23 =
-12х - 24
4) 16x(4x² - 5) + 17 - (4x + 1)(16x² - 4x + 1) =
64х³ - 80х + 17 - 64х³ - (16х + 4х + 16х² - 4х + 1) =
64х³ - 80х + 17 - 64х³ - 16х - 4х - 16х² + 4х - 1 =
64х³ - 64х³ - 16х² - 80х - 16х - 4х + 4х + 17 - 1 =
- 16х² - 96х + 16