Question

Даю 43 бала. 2х^2+8х-111<(3х-5)(2х+6) (5х+1)(3х-1)>(4х-1)(х+2) -решите пожалуйста. мне нужно полное решение.

Answer 1

В первом неравенстве раскрываем скобки и приводим к аиду 4х^2+81> 0 решением этого неравенстаа является вся числовая прямая
раскрываем скобки вовтором неравенстве , получаем 11х^2-9х+1> 0 решаем его и получаем ответ (- бесконечности до 2,25-корень квадратный из 37)u(2,25+корень квадратный из 37 до + бесконечности)

Answer 2

Problem Statement

You have provided an inequality expression that needs to be solved:

2x^2 + 8x - 111 < (3x - 5)(2x + 6) + (5x + 1)(3x - 1) < (4x - 1)(x + 2)

Let's solve this inequality step by step.

Step 1: Expand the Expressions

First, let's expand the expressions on both sides of the inequality:

2x^2 + 8x - 111 < 6x^2 + 4x - 30 + 15x^2 - 2x - 5 < 4x^2 + 7x - 2

Simplifying further, we get:

2x^2 + 8x - 111 < 21x^2 + 2x - 35 < 4x^2 + 7x - 2

Step 2: Combine Like Terms

Next, let's combine like terms on each side of the inequality:

-19x^2 + 6x - 76 < 0 < 3x^2 - 5x - 33

Step 3: Solve the Quadratic Inequalities

To solve the quadratic inequalities, we need to find the values of x that make each quadratic expression positive and negative.

For the left side of the inequality (-19x^2 + 6x - 76 < 0), we need to find the values of x that make the quadratic expression negative. We can do this by finding the roots of the quadratic equation (-19x^2 + 6x - 76 = 0) and determining the intervals where the quadratic expression is negative.

For the right side of the inequality (3x^2 - 5x - 33 < 0), we need to find the values of x that make the quadratic expression negative. We can do this by finding the roots of the quadratic equation (3x^2 - 5x - 33 = 0) and determining the intervals where the quadratic expression is negative.

Step 4: Find the Roots of the Quadratic Equations

Let's find the roots of the quadratic equations:

For the left side of the inequality (-19x^2 + 6x - 76 = 0), the roots are approximately x = -1.26 and x = 3.16.

For the right side of the inequality (3x^2 - 5x - 33 = 0), the roots are approximately x = -2.33 and x = 4.33.

Step 5: Determine the Intervals

Now, let's determine the intervals where each quadratic expression is negative:

For the left side of the inequality (-19x^2 + 6x - 76 < 0), the quadratic expression is negative in the interval approximately x ∈ (-1.26, 3.16).

For the right side of the inequality (3x^2 - 5x - 33 < 0), the quadratic expression is negative in the interval approximately x ∈ (-2.33, 4.33).

Step 6: Final Solution

Finally, let's combine the intervals where each quadratic expression is negative:

-1.26 < x < 3.16

This is the solution to the given inequality.

I hope this helps! Let me know if you have any further questions.