a大于0,b大于0证明 1.a+1/a大于等于2 2.(a+b)*(1/a+1/b)大于等于4(1/a+1/b)分之2小于等于跟号ab小于等于a+b/2小于等于跟号a^2+b^2/2a大于0b大于0.(1/a+1/b)分之2小于等于跟号ab小于等于a+b/2小于等
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![a大于0,b大于0证明 1.a+1/a大于等于2 2.(a+b)*(1/a+1/b)大于等于4(1/a+1/b)分之2小于等于跟号ab小于等于a+b/2小于等于跟号a^2+b^2/2a大于0b大于0.(1/a+1/b)分之2小于等于跟号ab小于等于a+b/2小于等](/uploads/image/z/565388-44-8.jpg?t=a%E5%A4%A7%E4%BA%8E0%2Cb%E5%A4%A7%E4%BA%8E0%E8%AF%81%E6%98%8E+1.a%2B1%2Fa%E5%A4%A7%E4%BA%8E%E7%AD%89%E4%BA%8E2+2.%EF%BC%88a%2Bb%EF%BC%89%2A%EF%BC%881%2Fa%2B1%2Fb%29%E5%A4%A7%E4%BA%8E%E7%AD%89%E4%BA%8E4%EF%BC%881%2Fa%2B1%2Fb%EF%BC%89%E5%88%86%E4%B9%8B2%E5%B0%8F%E4%BA%8E%E7%AD%89%E4%BA%8E%E8%B7%9F%E5%8F%B7ab%E5%B0%8F%E4%BA%8E%E7%AD%89%E4%BA%8Ea%2Bb%2F2%E5%B0%8F%E4%BA%8E%E7%AD%89%E4%BA%8E%E8%B7%9F%E5%8F%B7a%5E2%2Bb%5E2%2F2a%E5%A4%A7%E4%BA%8E0b%E5%A4%A7%E4%BA%8E0.%EF%BC%881%2Fa%2B1%2Fb%EF%BC%89%E5%88%86%E4%B9%8B2%E5%B0%8F%E4%BA%8E%E7%AD%89%E4%BA%8E%E8%B7%9F%E5%8F%B7ab%E5%B0%8F%E4%BA%8E%E7%AD%89%E4%BA%8Ea%2Bb%2F2%E5%B0%8F%E4%BA%8E%E7%AD%89)
a大于0,b大于0证明 1.a+1/a大于等于2 2.(a+b)*(1/a+1/b)大于等于4(1/a+1/b)分之2小于等于跟号ab小于等于a+b/2小于等于跟号a^2+b^2/2a大于0b大于0.(1/a+1/b)分之2小于等于跟号ab小于等于a+b/2小于等
a大于0,b大于0证明 1.a+1/a大于等于2 2.(a+b)*(1/a+1/b)大于等于4
(1/a+1/b)分之2小于等于跟号ab小于等于a+b/2小于等于跟号a^2+b^2/2
a大于0b大于0.(1/a+1/b)分之2小于等于跟号ab小于等于a+b/2小于等于跟号a^2+b^2/2这个怎么证明?
a大于0,b大于0证明 1.a+1/a大于等于2 2.(a+b)*(1/a+1/b)大于等于4(1/a+1/b)分之2小于等于跟号ab小于等于a+b/2小于等于跟号a^2+b^2/2a大于0b大于0.(1/a+1/b)分之2小于等于跟号ab小于等于a+b/2小于等
a+1/a-2=(a^2-2a+1)a=(a-1)^2/a>=0,故a+1/a>=0
(a+b)*(1/a+1/b)-4=((a+b)^2-4ab)/ab=(a^2+b^2+2ab-4ab)/ab=(a-b)^2/ab>=0,故a+b)*(1/a+1/b)大于等于4
a+1/a=(a*a+1)/a={(a-1)(a-1)+2a}/a=(a-1)(a-1)/a+2
因为(a-1)的平方大于等于0,a大于0,所以原式大于等于2
同理,第二小题展开后,a/b+b/a+2可以得a/b+b/a大于等于2。
1
(√a-1/√a)≥0 ,a+1/a≥2
2
(a+b)*(1/a+1/b)=2+[a/b+1/(a/b)]≥2+2
(a+b)*(1/a+1/b)≥4