Question

При каких значениях x верно x > x2

Answer 1

Когда х отрицательное число

Answer 2

Understanding the Inequality x > x^2

To understand the values of x for which the inequality x > x^2 is true, we can analyze the given inequality and determine the range of values for x that satisfy it.

Analyzing the Inequality

The inequality x > x^2 can be rewritten as x - x^2 > 0. This can be further simplified to x(1 - x) > 0.

Determining the Range of Values

To find the range of values for x that satisfy the inequality x(1 - x) > 0, we can use the concept of intervals and signs of the expression x(1 - x).

- When x < 0, both x and (1 - x) are negative, so the product x(1 - x) is positive. - When 0 < x < 1, x is positive and (1 - x) is negative, so the product x(1 - x) is negative. - When x > 1, both x and (1 - x) are positive, so the product x(1 - x) is positive.

Therefore, the inequality x > x^2 is true for the range of values of x that satisfy the condition x < 0 or x > 1.

Conclusion

In conclusion, the inequality x > x^2 is true for the values of x that are less than 0 or greater than 1.

- Source: ' ' - Source: ' , '