Re: [中學] 求證不等式
※ 引述《ej001 ( )》之銘言：
: a, b are all positive real number
: please prove
: {1 + a } b+1 { a }b
: {------} > {---}
: {1 + b } { b }
: thank you!
First of all, '>' is wrong, as two sides are equal when a=b.
So we are proving the case of '>=' instead.
b(1+a) (b+1)
<=> (--------) >= b/a
a(1+b)
<=> ( 1 + (b-a)/(ab+a))^(b+1) >= b/a.
note that (b-a)/(ab+a) > -a/(ab+a) > -1.
Thus, the result follows from the Bernoulli inequality.
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