The inequality x^2 - 2x > 0 has to be solved.

x^2 - 2x > 0

x(x - 2) > 0

This is true in two cases:

x > 0 and x - 2 > 0

x > 0 and x > 2

All values of x greater than 2 satisfy both the inequalities.

x < 0 and x - 2 < 0

x < 0 and x < 2

This is true when x < 0

The inequality x^2 - 2x > 0 is satisfied when x lies in the set `(-oo, 2)U(2, oo)`

To solve the inequality x^2-2x > 0.

Solution:

x^2-2x < 0 implies x(x-2) < 0. So if x is between the roots 0 and 2, then both factors areof opposite sign and the product x(x-2) is negative. So 0<x<2 . x(x-2) = 0 when x=0 or x=2. And x^2-2x = x(x-2) > 0 when x>3 or when x<2.

First of all, we'll solve the qudratic equation:

x^2 -2x = 0

We'll factorize to solve the equation.

x(x-2) = 0

x1=0, x2=2

We know that the expression is positive outside the roots, because the values of function have the same sign of the "a" coefficient, a=1, which is positive.

The inequality is positive when x belongs to the intervals (-inf.,0)U(2,+inf.).