Question

一道高中数学必修五均值不等式的一道题

Answer 1

(a+1/a)(b+1/b)

=(a^2+1)/a*(b^2+1)/b

=(a^2b^2+a^2+1+b^2)/ab

=[a^2b^2+(a+b)^2-2ab+1]/ab

=[a^2b^2+(1-2ab)+1]/ab

=[(ab-1)^2+1]/ab

(ab-1)^2+1≥25/16

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