Question

-25x^2<30x+9 решите пж

Answer 1

Ответ : x€ (-0,6; + бесконечность)
РЕШЕНИЕ НА ФОТО

Answer 2

To solve the inequality -25x^2 < 30x + 9, we need to find the values of x that satisfy the inequality. Here's the step-by-step solution:

Step 1: Move all terms to one side of the inequality to set it to zero: -25x^2 - 30x - 9 < 0

Step 2: To solve the quadratic inequality, we'll find the roots of the corresponding quadratic equation: -25x^2 - 30x - 9 = 0

Step 3: Solve the quadratic equation using factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula: The quadratic formula is given by x = (-b ± √(b^2 - 4ac)) / 2a.

For the equation -25x^2 - 30x - 9 = 0, the coefficients are: a = -25, b = -30, and c = -9.

Now, substitute the values into the quadratic formula:

x = (30 ± √((-30)^2 - 4 * (-25) * (-9))) / 2 * (-25) x = (30 ± √(900 - 900)) / -50 x = (30 ± √0) / -50 x = (30 ± 0) / -50

Step 4: Solve for x: a) x = (30 + 0) / -50 x = 0 / -50 x = 0

b) x = (30 - 0) / -50 x = 30 / -50 x = -3/5

Step 5: Now, we have the critical points (values of x where the expression equals zero): x = 0 and x = -3/5.

Step 6: Analyze the inequality based on these critical points.

• If x < -3/5, then -25x^2 is positive (since x^2 is positive), and 30x + 9 is negative. So, the whole expression -25x^2 - 30x - 9 will be positive.
• If -3/5 < x < 0, then -25x^2 is negative (since x^2 is positive), and 30x + 9 is negative. So, the whole expression -25x^2 - 30x - 9 will be negative.
• If x > 0, then -25x^2 is negative (since x^2 is positive), and 30x + 9 is positive. So, the whole expression -25x^2 - 30x - 9 will be negative.

Step 7: Put the information together to write the final solution:

The solution to the inequality -25x^2 < 30x + 9 is: x < -3/5 or x > 0.

In interval notation, the solution is (-∞, -3/5) ∪ (0, ∞).