已知a,b,c为正实数,且ab+bc+ca=1(1)求a+b+c-abc的最小值(2)证明:a^2/(a^2+1)+b^2/已知a,b,c为正实数,且ab+bc+ca=1(1)求a+b+c-abc的最小值(2)证明:a^2/(a^2+1)+b^2/(b^2+1)+c^2/(c^2+1)≥3/4

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已知a,b,c为正实数,且ab+bc+ca=1(1)求a+b+c-abc的最小值(2)证明:a^2/(a^2+1)+b^2/
已知a,b,c为正实数,且ab+bc+ca=1
(1)求a+b+c-abc的最小值
(2)证明:a^2/(a^2+1)+b^2/(b^2+1)+c^2/(c^2+1)≥3/4

min{a+b+c-a b c|a>0&&b>0&&c>0&&a b+a c+b c = 1} = 8/(3 sqrt(3))
at (a,b,c) = (1/sqrt(3),1/sqrt(3),1/sqrt(3))
min{a^2/(a^2+1)+b^2/(b^2+1)+c^2/(c^2+1)|a b+a c+b c = 1&&a>0&&b>0&&c>0} = 3/4
at (a,b,c) = (1/sqrt(3),1/sqrt(3),1/sqrt(3)) 证.