比较大小,说明理由:①(x+y)/2 ②根号下xy ③2xy/(x+y)

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比较大小,说明理由:①(x+y)/2 ②根号下xy ③2xy/(x+y)
比较大小,说明理由:①(x+y)/2 ②根号下xy ③2xy/(x+y)

比较大小,说明理由:①(x+y)/2 ②根号下xy ③2xy/(x+y)
(√x+(√y)^2 = x+y-2(√xy)>=0
(x+y)/2>=(√xy)
2/(x+y)<=1/(√xy)=(√xy)/xy
2xy/(x+y)<=(√xy)
即(x+y)/2>=(√xy)>=2xy/(x+y)