高二数学推理与证明习题!1.已知:a>0,b>0,求证2ab/a+b≤√ab≤a+b/2≤√[(a^2+b^2)/2]2.设a,b,c∈R,求证√(a^2+b^2)+√(b^2+c^2)+√(c^2+a^2)≥√2(a+b+c)3.证明:f(x)=2^(x²-4x+3)在(2,+∞)上是增加
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![高二数学推理与证明习题!1.已知:a>0,b>0,求证2ab/a+b≤√ab≤a+b/2≤√[(a^2+b^2)/2]2.设a,b,c∈R,求证√(a^2+b^2)+√(b^2+c^2)+√(c^2+a^2)≥√2(a+b+c)3.证明:f(x)=2^(x²-4x+3)在(2,+∞)上是增加](/uploads/image/z/2085430-22-0.jpg?t=%E9%AB%98%E4%BA%8C%E6%95%B0%E5%AD%A6%E6%8E%A8%E7%90%86%E4%B8%8E%E8%AF%81%E6%98%8E%E4%B9%A0%E9%A2%98%211.%E5%B7%B2%E7%9F%A5%EF%BC%9Aa%EF%BC%9E0%2Cb%EF%BC%9E0%2C%E6%B1%82%E8%AF%812ab%2Fa%2Bb%E2%89%A4%E2%88%9Aab%E2%89%A4a%2Bb%2F2%E2%89%A4%E2%88%9A%5B%28a%5E2%2Bb%5E2%29%2F2%5D2.%E8%AE%BEa%2Cb%2Cc%E2%88%88R%2C%E6%B1%82%E8%AF%81%E2%88%9A%28a%5E2%2Bb%5E2%29%2B%E2%88%9A%28b%5E2%2Bc%5E2%29%2B%E2%88%9A%28c%5E2%2Ba%5E2%29%E2%89%A5%E2%88%9A2%EF%BC%88a%2Bb%2Bc%EF%BC%893.%E8%AF%81%E6%98%8E%EF%BC%9Af%EF%BC%88x%EF%BC%89%3D2%5E%EF%BC%88x%26%23178%3B-4x%2B3%EF%BC%89%E5%9C%A8%EF%BC%882%2C%2B%E2%88%9E%EF%BC%89%E4%B8%8A%E6%98%AF%E5%A2%9E%E5%8A%A0)
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