Pa con zup v0j

N

nguyenminh44

[tex]\frac{1}{(x-y)^2}+\frac{1}{(y-z)^2}+\frac{1}{(z-x)^2}\geq\frac{9}{2(x^2+y^2+z^2)} \Leftrightarrow 2(x^2+y^2+z^2)(\frac{1}{(x-y)^2}+\frac{1}{(y-z)^2}+\frac{1}{(z-x)^2})\geq9 [/tex]

Do [tex]2(x^2+y^2+z^2)=x^2+y^2+y^2+z^2+z^2+x^2\geq(x-y)^2+(y-z)^2+(z-x)^2[/tex]

Nên VT[tex]\geq[(x-y)^2+(y-z)^2+(z-x)^2](\frac{1}{(x-y)^2}+\frac{1}{(y-z)^2}+\frac{1}{(z-x)^2})\geq9[/tex] (Cauchy 2 thừa số)
 
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