Question

X^2 - 4x - 21 > 0 помогите

Answer 1

X²-4x-21 >0
x²-4x-21=0
D=b²-4ac=4²-4×1×(-21)=16+84=100 √100=10
x1=(4+10):2=7
x2=(4-10):2=-4
Я думою, что так!

Answer 2

Solving the Inequality x^2 - 4x - 21 > 0

To solve the inequality x^2 - 4x - 21 > 0, we can use the method of finding the critical points and testing the intervals.

1. Finding the Critical Points: To find the critical points, we first factorize the quadratic expression. The critical points are the points where the expression equals zero.

The quadratic expression x^2 - 4x - 21 can be factorized as (x - 7)(x + 3).

Therefore, the critical points are x = 7 and x = -3.

2. Testing the Intervals: We can test the intervals created by the critical points to determine the solution to the inequality.

- Test the interval (-∞, -3): Choose a test point, for example, x = -4. Substituting x = -4 into the expression x^2 - 4x - 21 gives a positive value.

- Test the interval (-3, 7): Choose a test point, for example, x = 0. Substituting x = 0 into the expression x^2 - 4x - 21 gives a negative value.

- Test the interval (7, +∞): Choose a test point, for example, x = 8. Substituting x = 8 into the expression x^2 - 4x - 21 gives a positive value.

3. Conclusion: From the tests, we can conclude that the solution to the inequality x^2 - 4x - 21 > 0 is: x < -3 or x > 7.