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Let a and B be positive numbers, and prove the following inequality (1.) B / A + A / b ≥ 2 (2.) a + 1 / a ≥ 2
a. B is a positive number
（1.）
B / A + A / b = {root (B / a) - root (A / b)} ^ 2 + 2 root {(B / a) (A / b)} = {root (B / a) - root (A / b)} ^ 2 + 2 ≥ 2
≥2
（2.）
A + 1 / a = {root (a) - root (1 / a)} ^ 2 + 2 root {(a) (1 / a)} = {root (a) - root (1 / a)} ^ 2 + 2 ≥ 2
≥2
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