已知abc均为正实数,求证b²/a+c²/b+a²/c≥c√b/a+a√c/b+b√a/c
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![已知abc均为正实数,求证b²/a+c²/b+a²/c≥c√b/a+a√c/b+b√a/c](/uploads/image/z/2770684-52-4.jpg?t=%E5%B7%B2%E7%9F%A5abc%E5%9D%87%E4%B8%BA%E6%AD%A3%E5%AE%9E%E6%95%B0%2C%E6%B1%82%E8%AF%81b%26%23178%3B%2Fa%EF%BC%8Bc%26%23178%3B%2Fb%EF%BC%8Ba%26%23178%3B%2Fc%E2%89%A5c%E2%88%9Ab%2Fa%EF%BC%8Ba%E2%88%9Ac%2Fb%EF%BC%8Bb%E2%88%9Aa%2Fc)
已知abc均为正实数,求证b²/a+c²/b+a²/c≥c√b/a+a√c/b+b√a/c
已知abc均为正实数,求证b²/a+c²/b+a²/c≥c√b/a+a√c/b+b√a/c
已知abc均为正实数,求证b²/a+c²/b+a²/c≥c√b/a+a√c/b+b√a/c
2(b²/a+c²/b+a²/c)=(b^2/a+a^2/c)+(c^2/b+b²/a)+(a^2/c+c^2/b)>=2
√(b^2/a)*(a^2/c)+2√(c^2/b)*(b²/a)+2√(a^2/c)*(c^2/b)=2(b√a/c+c√b/a+a√c/b),即b²/a+c²/b+a²/c≥c√b/a+a√c/b+b√a/c.