Let x ≥ 0 and y ≥ 0 be arbitrary real numbers. The arithmetic mean of x and y is (x + y)/2, their average. The geometric mean of x and y is √xy 1.First, a warm-up exercise: prove that x2 ≥ 0 for any...

Let x ≥ 0 and y ≥ 0 be arbitrary real numbers. The arithmetic mean of x and y is (x + y)/2, their average. The geometric mean of x and y is √xy

1.First, a warm-up exercise: prove that x2 ≥ 0 for any real number x. (Hint: yes, it’s easy.)