If A.M and G.M are Arithmetic and Geometric mean then prove that A.M is (greater than or equal to)G.M.?

A.M. of two positive real numbers a and b = (a + b)/2
G.M. of two positive real numbers a and b = √(ab)

(A.M.)² - (G.M.)²
= [(a + b)/2]² - (√ab)²
= (1/2)²(a + b)² - ab
= (1/4)(a² + 2ab + b²) - (1/4)(4ab)
= (1/4)[(a² + 2ab + b²) - 4ab]
= (1/4)[a² + 2ab + b² - 4ab]
= (1/4)[a² - 2ab + b²]
= (1/4)(a - b)² ≥ 0 for all positive real numbers a and b

Since (A.M.)² - (G.M.)² ≥ 0
then (A.M.)² ≥ (G.M.)²
and thus A.M. ≥ G.M.

I can't because it isn't always the case.

Example:
-8 and -2

Arithmetic mean:
(-8 + -2) / 2 = -5
-8, -5, -2

Geometric mean:
√(-8 * -2) = ± 4
-8, -4, -2

-5 < -4