Monday, October 26, 2009

AM, GM inequality

d1, d2, d3 and d4 are different digits, whether 0.d1d2 + 0.d3d4 > 1

(1) the least among d1,d2,d3, d4 is 4.
(2) (0.d1d2)(0.d3d4) > 0.5

(1). The least possible 0.46 + 0.57 > 1 suff
(2) a+b >= 2sqrt(ab) AM >= GM
ab > 0.5 and a n b are +ve.
sqrt(ab) > 1/sqrt(2)
a+b >= 2/sqrt(2)
a +b >= sqrt(2) = 1.414


Suff

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