Question

X2- 8x + 25 > 0 x2 - 49 50<0​

Answer 1

Ответ:

а)x принадлежит любому(отрицательный дискриминант)

б)x (-15√22;15√22)

Объяснение:

Answer 2

To solve the inequality x^2 - 8x + 25 > 0, we can follow these steps:

Step 1: Factorize the quadratic expression if possible. In this case, the quadratic expression x^2 - 8x + 25 cannot be factored.

Step 2: Find the roots of the quadratic equation x^2 - 8x + 25 = 0. We can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a). Plugging in the values a = 1, b = -8, and c = 25, we get:

x = (-(-8) ± √((-8)^2 - 4(1)(25))) / (2(1)) x = (8 ± √(64 - 100)) / 2 x = (8 ± √(-36)) / 2

The discriminant (√(b^2 - 4ac)) under the square root is negative, indicating that there are no real solutions. Therefore, the quadratic equation x^2 - 8x + 25 = 0 has no real roots.

Step 3: Analyze the inequality based on the roots. Since the quadratic equation has no real roots, it means that the parabola represented by the quadratic expression x^2 - 8x + 25 does not intersect the x-axis. Thus, the expression x^2 - 8x + 25 is always greater than zero (positive) for all real values of x.

Therefore, the inequality x^2 - 8x + 25 > 0 is true for all real values of x.

Now, let's solve the inequality x^2 - 49 < 50:

Step 1: Simplify the expression on the left side: x^2 - 49 + 50 < 0 becomes x^2 + 1 < 0.

Step 2: Since x^2 is always greater than or equal to zero for real values of x, there are no real solutions to the inequality x^2 + 1 < 0. Thus, the inequality is not satisfied for any real value of x.

In summary:

• The inequality x^2 - 8x + 25 > 0 is true for all real values of x.
• The inequality x^2 - 49 < 50 is not satisfied for any real value of x.