How to prove that (a + 1 / a) (B + 1 / b) is greater than or equal to 25 / 4?

(a-1)² ≧ 0
a² -2a + 1 ≧ 0
a² + 1 ≧ 2a
a + 1/a ≧ 2
Similarly, B + 1 / b ≥ 2
therefore
(a+1/a)(b+1/b) ≧ 2*2
(a+1/a)(b+1/b) ≧ 4

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