(x-2)^((x^2)-6x+8)>1

Предыдущий
вопрос Следующий
вопрос

To find the values of x for which the given inequality holds true, we can first determine when the expression (x-2)^(x^2-6x+8) equals 1.

When (x-2)^(x^2-6x+8) equals 1, this means that the base (x-2) must be equal to 1, and the exponent (x^2-6x+8) can be any integer value.

Therefore, we have:

x - 2 = 1
x = 3

Now, we need to consider when the expression is greater than 1. Since the base (x-2) is greater than 1 for x > 3, the expression will always be greater than 1 for x > 3.

Therefore, the solutions to the inequality (x-2)^(x^2-6x+8) > 1 are all real numbers greater than 3, or simply x > 3.