① A > O, b > O, and a + B = 1, prove that (a + 1 / a) (B + 1 / b) is greater than or equal to 25 / 4 ② A, B belong to R and a is not equal to B. prove {1 + (square of a)} - under | root {1 + (square of B)}| | Math enthusiast | Mathematical art

① A > O, b > O, and a + B = 1, prove that (a + 1 / a) (B + 1 / b) is greater than or equal to 25 / 4 ② A, B belong to R and a is not equal to B. prove {1 + (square of a)} - under | root {1 + (square of B)}|

1. Left formula = AB + A / B + 1 / AB + B / A
=(a2b2+a2+1+b2)/ab
=[a2b2+(1-2ab)+1]/ab
=[(ab-1)2+1]/ab
(ab-1)2+1≥25/16,0

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