The number of distinct solutions of the equation |x|2 – 6|x| + 9 = 0 is:

The given equation is |x|² - 6|x| + 9 = 0.

This equation is in the form of a quadratic equation, where |x| is the variable.

The quadratic equation is of the form ax² - bx + c = 0.

Here, a = 1, b = -6, and c = 9.

The number of distinct solutions of a quadratic equation is given by the discriminant, D = b² - 4ac.

Let's calculate the discriminant:

D = (-6)² - 419 D = 36 - 36 D = 0

When the discriminant is equal to zero, the quadratic equation has exactly one distinct solution.

Therefore, the equation |x|² - 6|x| + 9 = 0 has exactly one distinct solution.