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Solution Observe that (a+2b−3c)+(b+2c−3a )+(c+2a−3b)=0. Because ... (a-b)+(b-c)+(c-a)= 3\sqrt[3]{(a-b)(b-c)(c-a)}. ... \frac{(x+y+z)^{2}}{x^ {2}+y^{2}+z^{2}+5(xy+xz+yz)}\geq\frac{1}{2},.
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