Question

помогите решить систему неравенств 4x^2+9x-9 < или равно 0,х-1/2<0.

Answer 1

решим уравнение х1=(-9+15)/8=3/4 x2=-3

[-3;3/4]

второе неравенство х<1/2

решение системы

[-3;1/2)

Answer 2

е х1=(-9+15)/8=3/4 x2=-    [-3;3/4]   [-3;1/2)

Answer 3

Solving the System of Inequalities

To solve the system of inequalities 4x^2 + 9x - 9 ≤ 0 and x - 1/2 < 0, we'll start by solving each inequality separately and then finding the intersection of their solutions.

Solving the Inequality 4x^2 + 9x - 9 ≤ 0

The inequality 4x^2 + 9x - 9 ≤ 0 represents a quadratic inequality. We can solve it by finding the roots of the corresponding quadratic equation 4x^2 + 9x - 9 = 0 and then determining the intervals where the inequality is satisfied.

The roots of the quadratic equation can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

where a = 4, b = 9, and c = -9.

The discriminant Δ = b^2 - 4ac is used to determine the nature of the roots.

The roots of the quadratic equation will help us identify the intervals where the inequality is satisfied.

Solving the Inequality x - 1/2 < 0

The inequality x - 1/2 < 0 is a simple linear inequality. We can solve it by isolating the variable x.

Finding the Intersection of Solutions

After solving both inequalities, we'll find the intersection of their solutions to determine the values of x that satisfy both inequalities simultaneously.

Let's proceed with solving the inequalities and finding their intersection.