Solve the Quadratic Inequality: x²-6x+9>0

To solve the quadratic inequality $x^2 - 6x + 9 > 0$, we first rewrite the quadratic expression in a recognizable form:

The expression can be rewritten as:

$x^2 - 6x + 9 = (x-3)^2$

This is a perfect square trinomial, where $(x-3)^2 > 0$. We know that a square of a real number is only greater than zero when the number itself is not zero.

Thus, $(x-3)^2 > 0$ implies $x - 3 \neq 0$, meaning $x \neq 3$.

Consequently, the inequality $x^2 - 6x + 9 > 0$ holds true for all $x$ except $x = 3$.

Therefore, the solution to the inequality is:

$3 \neq x$