Question

1) 13 + x²(x – 9) <(x - 3) + 11; 2) 26 + (2 + x)^3 < x^2 (6 + x);3) 3x - x²(15 + x) > -(x + 5)^3 – 4x;4) (4 + x)^3 - 6x < x²(x + 12) + 1.​

Answer 1

1)13+x²(x-9)≤(x-3)³+11

13+x³-9x²≤x³-3*x²*3+3*x*3²-3³

13+x³-9x²≤x³-9x²+27x-27

x³-9x²-x³+9x²-27x≤-27-13

-27x≤-40

x≤1 13/27

(-∞;1 13/27]

2)26+(2+x)³26+2³+3*2²*x+3*2*x²+x³<6x²+x³

26+8+12x+6x²+x³<6x²+x³

12x+6x²+x³-6x²-x³<-26-8

12x<-34

x<-2 10/12

(-∞;-2 10/12)

Объяснение:

Answer 2

To solve these inequalities, we'll follow the steps to isolate the variable x. Let's go through each one:

1. $13 + x^2(x - 9) < (x - 3) + 11$

First, simplify both sides of the inequality:

$13 + x^3 - 9x^2 < x - 3 + 11$

Now, combine like terms:

$x^3 - 9x^2 + 13 < x + 8$

Subtract $x + 8$ from both sides:

$x^3 - 9x^2 - x - 8 + 13 < 0$

$x^3 - 9x^2 - x + 5 < 0$

Now, we need to find the roots of the equation $x^3 - 9x^2 - x + 5 = 0$. This equation doesn't have a simple analytical solution, so we'll need to use numerical methods or graphing software to find the roots. Let's denote these roots as $x_1$, $x_2$, and $x_3$.

The solution to the inequality is:

$-\infty < x < x_1$ or $x_2 < x < x_3$

2. $26 + (2 + x)^3 < x^2 (6 + x)$

First, expand both sides of the inequality:

$26 + 8 + 12x + x^3 < 6x^2 + x^3$

Now, move all terms to one side to set the inequality to zero:

$0 < 6x^2 + x^3 - 12x - 26$

Now, we need to find the roots of the equation $6x^2 + x^3 - 12x - 26 = 0$. This equation doesn't have a simple analytical solution, so we'll need to use numerical methods or graphing software to find the roots. Let's denote these roots as $x_1$, $x_2$, and $x_3$.

The solution to the inequality is:

$-\infty < x < x_1$ or $x_2 < x < x_3$

3. $3x - x^2(15 + x) > -(x + 5)^3 - 4x$

First, simplify both sides of the inequality:

$3x - 15x^2 - x^3 > -(x + 5)^3 - 4x$

Now, move all terms to one side to set the inequality to zero:

$0 > -x^3 - 15x^2 + 3x - (x + 5)^3 - 4x$

Simplify further:

$0 > -x^3 - 15x^2 + 3x - (x + 5)^3 - 4x$

Now, we need to find the roots of the equation $0 > -x^3 - 15x^2 + 3x - (x + 5)^3 - 4x$. This equation doesn't have a simple analytical solution, so we'll need to use numerical methods or graphing software to find the roots. Let's denote these roots as $x_1$, $x_2$, and $x_3$.

The solution to the inequality is:

$x_1 < x < -5$ or $x_2 < x < x_3$