Question

7x-x^2>0 срочно помогите пожалуйста

Answer 1

7х-х²>0
x(7-x)>0
x1>0
7-x>0
x2<7

Answer 2

Solving the Inequality 7x - x^2 > 0

To solve the inequality 7x - x^2 > 0, we can factorize it and find the critical points to determine the intervals where the inequality holds true.

Factoring the Inequality

The inequality 7x - x^2 > 0 can be rewritten as -x^2 + 7x > 0. To factorize it, we can factor out -x: - x(-x + 7) > 0

Finding Critical Points

To find the critical points, we set each factor equal to zero and solve for x: - Setting -x = 0 gives x = 0 - Setting -x + 7 = 0 gives x = 7

Determining Intervals

Now, we can use these critical points to determine the intervals where the inequality holds true. We create a sign chart to analyze the inequality: - Test a value less than 0, such as x = -1: -(-1)(-1 + 7) = -1(6) = -6 < 0 - Test a value between 0 and 7, such as x = 3: -(3)(3 - 7) = -3(-4) = 12 > 0 - Test a value greater than 7, such as x = 8: -(8)(8 - 7) = -8(1) = -8 < 0

Conclusion

From the sign chart analysis, we can conclude that the inequality -x^2 + 7x > 0 holds true for the intervals: - x < 0 - 0 < x < 7

Therefore, the solution to the inequality 7x - x^2 > 0 is x < 0 and 0 < x < 7.