a+b+c=1(a>0,b>0,c>0),求证:(1+a)(a+b)(1+c)>=8(1-a)(1-b)(1-c)已知:a+b+c=1(a>0,b>0,c>0)求证:(1+a)(a+b)(1+c)>=8(1-a)(1-b)(1-c)
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![a+b+c=1(a>0,b>0,c>0),求证:(1+a)(a+b)(1+c)>=8(1-a)(1-b)(1-c)已知:a+b+c=1(a>0,b>0,c>0)求证:(1+a)(a+b)(1+c)>=8(1-a)(1-b)(1-c)](/uploads/image/z/10736962-34-2.jpg?t=a%2Bb%2Bc%3D1%EF%BC%88a%3E0%2Cb%3E0%2Cc%3E0%EF%BC%89%2C%E6%B1%82%E8%AF%81%EF%BC%9A%EF%BC%881%2Ba%EF%BC%89%EF%BC%88a%2Bb%EF%BC%89%EF%BC%881%2Bc%EF%BC%89%3E%3D8%281-a%29%281-b%29%281-c%29%E5%B7%B2%E7%9F%A5%EF%BC%9Aa%2Bb%2Bc%3D1%EF%BC%88a%3E0%2Cb%3E0%2Cc%3E0%EF%BC%89%E6%B1%82%E8%AF%81%EF%BC%9A%EF%BC%881%2Ba%EF%BC%89%EF%BC%88a%2Bb%EF%BC%89%EF%BC%881%2Bc%EF%BC%89%3E%3D8%281-a%29%281-b%29%281-c%29)
a+b+c=1(a>0,b>0,c>0),求证:(1+a)(a+b)(1+c)>=8(1-a)(1-b)(1-c)已知:a+b+c=1(a>0,b>0,c>0)求证:(1+a)(a+b)(1+c)>=8(1-a)(1-b)(1-c)
a+b+c=1(a>0,b>0,c>0),求证:(1+a)(a+b)(1+c)>=8(1-a)(1-b)(1-c)
已知:a+b+c=1(a>0,b>0,c>0)
求证:(1+a)(a+b)(1+c)>=8(1-a)(1-b)(1-c)
a+b+c=1(a>0,b>0,c>0),求证:(1+a)(a+b)(1+c)>=8(1-a)(1-b)(1-c)已知:a+b+c=1(a>0,b>0,c>0)求证:(1+a)(a+b)(1+c)>=8(1-a)(1-b)(1-c)
左式=(1+a)(1+b)(1+c)
=(a+b+c+a)(a+b+c+b)(a+b+c+c)
=[(a+b)+(a+c)][(a+b)+(b+c)][(a+c)+(b+c)]
≥2√(a+b)√(a+c)·2√(a+b)√(b+c)·2√(a+c)√(b+c) (由均值不等式)
=8(b+c)(a+b)(a+c)
=8(1-a)(1-b)(1-c)=右式
原式是:(1+a)(a+b)(1+c)
左式=(1+a)(1+b)(1+c) 不等吧....除非题出错了..