Question

-6х²+13х-5≥021х²-22х+7>0х²-3.5х-2≤0​

Answer 1

Объяснение:

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Answer 2

To solve the inequalities -6x² + 13x - 5 ≥ 0 and 21x² - 22x + 7 > 0, as well as the inequality 0x² - 3.5x - 2 ≤ 0, you can follow these steps:

1. Solve the quadratic equation -6x² + 13x - 5 = 0 to find the critical points (where the quadratic is equal to zero):

   -6x² + 13x - 5 = 0

   You can use the quadratic formula to find the solutions:

   x = [ -b ± √(b² - 4ac) ] / (2a)

   For this equation, a = -6, b = 13, and c = -5.

   x = [ -13 ± √(13² - 4*(-6)(-5)) ] / (2(-6)) x = [ -13 ± √(169 + 120) ] / (-12) x = [ -13 ± √289 ] / (-12) x = [ -13 ± 17 ] / (-12)

   So, the solutions are:

   x₁ = (17 - 13) / (-12) = 1/3 x₂ = (-17 - 13) / (-12) = -5/2

2. Now, you have the critical points x = 1/3 and x = -5/2. These are the points where the inequalities may change.

3. Analyze the sign of the inequalities in the regions defined by the critical points.

   a. For -6x² + 13x - 5 ≥ 0:

   -6x² + 13x - 5 is a downward-opening parabola. The roots are at x = 1/3 and x = -5/2. So, in the intervals (-∞, -5/2), (-5/2, 1/3), and (1/3, ∞), the inequality is true. So, the solution to this inequality is:

   x ≤ -5/2 or -5/2 < x ≤ 1/3 or x > 1/3

   b. For 21x² - 22x + 7 > 0:

   21x² - 22x + 7 is an upward-opening parabola. The roots are at x = 1/3 and x = -5/2. So, in the intervals (-∞, -5/2) and (1/3, ∞), the inequality is true. So, the solution to this inequality is:

   x < -5/2 or x > 1/3

4. Finally, for the inequality 0x² - 3.5x - 2 ≤ 0, it's a linear equation, and you can find the solution by solving it directly:

   -3.5x - 2 ≤ 0

   Add 2 to both sides:

   -3.5x ≤ 2

   Divide by -3.5, remembering to reverse the inequality when dividing by a negative number:

   x ≥ -2/3.5

   x ≥ -4/7

   So, the solution to this inequality is:

   x ≥ -4/7

In summary, the solutions to the given inequalities are:

-6x² + 13x - 5 ≥ 0: x ≤ -5/2 or -5/2 < x ≤ 1/3 or x > 1/3 21x² - 22x + 7 > 0: x < -5/2 or x > 1/3 0x² - 3.5x - 2 ≤ 0: x ≥ -4/7