Question

2X+8X*(2X+3)>-5+9x это сколько?

Answer 1

$2x+16x^2+24x+5-9x\ \textgreater \ 0 \\ 16x^2+17x+5\ \textgreater \ 0 \\ D=17^2-4\times16\times5=-31$
парабола никогда не пересекает ось абсцисс, значит x∈(-∞;+∞)

Answer 2

To solve the inequality 2X + 8X * (2X + 3) > -5 + 9X, we'll first simplify the expression and then solve for X. Here's the step-by-step solution:

1. Distribute the multiplication: 2X + 8X * 2X + 8X * 3 > -5 + 9X

2. Simplify the terms: 2X + 16X^2 + 24X > -5 + 9X

3. Move all terms to one side of the inequality: 16X^2 + 24X + 2X - 9X + 5 > 0

4. Combine like terms: 16X^2 + 17X + 5 > 0

Now, we have a quadratic inequality in the form of Ax^2 + Bx + C > 0. To solve this, we can find the critical points and analyze the sign of the expression within different intervals.

Let's find the critical points (where the expression equals 0): 16X^2 + 17X + 5 = 0

Using the quadratic formula: X = (-B ± √(B^2 - 4AC)) / 2A X = (-(17) ± √((17)^2 - 4 * 16 * 5)) / (2 * 16) X = (-17 ± √(289 - 320)) / 32 X = (-17 ± √(-31)) / 32

Since the discriminant (B^2 - 4AC) is negative, the quadratic equation has no real solutions, which means there are no critical points for this inequality.

Next, we need to find the intervals where the expression is positive (greater than zero) to satisfy the inequality. Since the coefficient of X^2 (A) is positive (16), the parabola opens upwards, and the expression will be positive either on both sides of the parabola or not at all.

Therefore, the solution to the inequality is that the expression is greater than zero for all real values of X:

16X^2 + 17X + 5 > 0 for all X ∈ ℝ

This means that the inequality holds true for any real value of X.