Given that a > 0, b > 0, a + B = 1, it is proved that (a + 1 / a) (B + 1 / b) is greater than or equal to 25 / 4

Given that a > 0, b > 0, a + B = 1, it is proved that (a + 1 / a) (B + 1 / b) is greater than or equal to 25 / 4

a+b≥2√ab
ab≤1/4
(a+1/a)(b+1/b)
=(a^2+1)/a*(b^2+1)/b
=[a^2b^2+(1-2ab)+1]/ab
=[(ab-1)^2+1]/ab
(ab-1)^2+1≥25/16
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