23.证明:(1)a、b、c均为正实数,则a+b≥2√ab>0,ab+c2≥2√ab2>0(a+b)(ab+c2)≥4abe,当且仅当a=b=c时取等号5分(2)由柯西不等式有1+=((1·a+1+1√b+1+1+1)≤(1+F+(a+1+b+1+c+1)=18又a+b+c=3故√a+1+√6+1+√+1≤32,当且仅当a=b=c=1时取等号…10分

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