Question

Решить неравенства a)3x(2x-1)-6x²>2-x b) 12y²-(3y+4)4y>y-10) v)(1+3x)(3x-1)>6x+9² g) (4x-3)(3+4x)+x<16x²

Answer 1

Объяснение:

А) 3x×2x - 3x×1 - 6x^2>2 - x

6x^2 - 3x - 6x^2>2 - x

- 3x>2 - x

- 2x>2

- x>1

x<-1

Б) 12y^2 - 3y×4y - 4×4y>y - 10

12y^2 - 12y^2 - 16y>y - 10

- 16y - y>-10

- 17y>-10

- y>-10/17

y<10/17

В) 3x×1 + 9x^2 - 3x×1 - 1×1>6x+9x^2

- 1>6x

x<-1/6

Г) 4x×3 + 16x^2 - 4x×3 - 9 + x<16x^2

- 9 + x<0

x<9

Answer 2

a) 3x(2x-1) - 6x² > 2 - x

Let's simplify and solve the inequality step by step:

3x(2x-1) - 6x² > 2 - x 6x² - 3x - 6x² > 2 - x -3x > 2 - x -3x + x > 2 -2x > 2 x < 2/(-2) x < -1

Therefore, the solution to the inequality is x < -1.

b) 12y² - (3y+4)4y > y - 10

Let's simplify and solve the inequality step by step:

12y² - 12y² - 16y > y - 10 -16y > y - 10 -16y - y > -10 -17y > -10 y < (-10)/(-17) y < 10/17

Therefore, the solution to the inequality is y < 10/17.

v) (1+3x)(3x-1) > 6x + 9²

Let's simplify and solve the inequality step by step:

(1+3x)(3x-1) > 6x + 81 3x² - x + 3x - 1 > 6x + 81 3x² + 2x - 1 > 6x + 81 3x² - 4x - 82 > 0

To solve this quadratic inequality, we can find its roots:

3x² - 4x - 82 = 0

Using the quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), where a = 3, b = -4, and c = -82.

x = (4 ± √((-4)² - 4(3)(-82))) / (2(3)) x = (4 ± √(16 + 984)) / 6 x = (4 ± √1000) / 6 x = (4 ± 10√10) / 6 x = (2/3) ± (5/3)√10

Therefore, the solutions to the inequality are:

x < (2/3) - (5/3)√10 or x > (2/3) + (5/3)√10

g) (4x-3)(3+4x) + x < 16x²

Let's simplify and solve the inequality step by step:

(4x-3)(3+4x) + x < 16x² 12x² + 16x² - 9 - 12x + 3x + x < 16x² 28x² - 8x - 9 < 16x² 28x² - 16x² - 8x - 9 < 0 12x² - 8x - 9 < 0

To solve this quadratic inequality, we can find its roots:

12x² - 8x - 9 = 0

Using the quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), where a = 12, b = -8, and c = -9.

x = (8 ± √((-8)² - 4(12)(-9))) / (2(12)) x = (8 ± √(64 + 432)) / 24 x = (8 ± √496) / 24 x = (2/3) ± (√124) / 3 x = (2/3) ± (2/3)√31

Therefore, the solutions to the inequality are:

x < (2/3) - (2/3)√31 or x > (2/3) + (2/3)√31