The number x is an integer such that x^2 > x^3. What can you conclude about the value of x??
X is a negative number?
.5^2 = .25
.5^3 = .125
see :)
To determine what we can conclude about the value of x given that x^2 > x^3, let's break down the problem.
We know that x^2 represents x raised to the power of 2, and x^3 represents x raised to the power of 3. So, the inequality x^2 > x^3 can be rewritten as x^2 - x^3 > 0.
Now, we can simplify this expression further by factoring out an x^2 term: x^2(1 - x) > 0.
To solve this inequality, we need to consider two cases:
Case 1: When x^2 > 0
In this case, x^2 is positive, which means that the inequality 1 - x > 0 must hold true for x^2 - x^3 to be greater than 0. Solving 1 - x > 0, we find x < 1.
Case 2: When x^2 < 0
In this case, x^2 is negative. However, if x^2 < 0, then x must also be negative. So, x < 0.
Combining the conclusions from both cases, we can say that the value of x must be negative (x < 0) and less than 1 (x < 1) for the inequality x^2 > x^3 to hold true.