Question

(x-1)(3-2x)>-6 Скажите решение срочно

Answer 1

-2х²+5х+3>0

-2х²+5х+3=0

Д= 25+24=49=7²

х₁=-5+7/-4=-0.5

х²=-5-7/-4 = 3

Ответ: х принадлежащее (-0.5;3)

Answer 2

Solving the Inequality (x-1)(3-2x) > -6

To solve the inequality (x-1)(3-2x) > -6, we can follow these steps:

1. Expand and simplify the expression (x-1)(3-2x). 2. Set the expression greater than -6 and solve for x.

Step 1: Expand and Simplify the Expression

The expression (x-1)(3-2x) can be expanded as follows:

(x-1)(3-2x) = 3x - 2x^2 - 3 + 2x

Simplifying further, we get:

3x - 2x^2 - 3 + 2x = -2x^2 + 5x - 3

Step 2: Set the Expression Greater Than -6 and Solve for x

Now, we set the expression -2x^2 + 5x - 3 greater than -6:

-2x^2 + 5x - 3 > -6

Adding 6 to both sides:

-2x^2 + 5x + 3 > 0

This is a quadratic inequality. To solve it, we can find the roots of the corresponding equation -2x^2 + 5x + 3 = 0 and then test the intervals between the roots.

Let's find the roots of the equation -2x^2 + 5x + 3 = 0:

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

Where a = -2, b = 5, and c = 3.

The discriminant (b^2 - 4ac) is calculated as follows: b^2 - 4ac = 5^2 - 4*(-2)*3 = 25 + 24 = 49

The roots are then given by: x = (-(5) ± √(49)) / (2*(-2))

Solving for x, we get: x = (-(5) ± 7) / (-4)

So the roots are: x = (-(5) + 7) / (-4) = 2 / (-4) = -1/2 x = (-(5) - 7) / (-4) = -12 / (-4) = 3

Now, we can test the intervals between the roots to find the solution set for the inequality.

The solution set is: x < -1/2 or x > 3

Therefore, the solution to the inequality (x-1)(3-2x) > -6 is: x < -1/2 or x > 3.