a,b,c∈\rm R^+, $$abc=8.\,\,\, 求证:1a+1+1b+1+1c+1<2\dfrac{1}{\sqrt{a+1}}+\dfrac{1}{\sqrt{b+1}}+\dfrac{1}{\sqrt{c+1}}<2a+11+b+11+c+11<2.
P.S.P.S.P.S.明天就要数学高联了,打个卡qwq