Question

[Hoàng Thế Hải]

Cho (x+y+z)^2= x^2+y^2+z^2  CMR: 1/x^3+1/y^3+1/z^3= 3/xyz

Answer 1

[Gái FA]

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Answer 2

[Pham Van Hung]

   \(\left(x+y+z\right)^2=x^2+y^2+z^2\)

\(\Rightarrow x^2+y^2+z^2+2\left(xy+yz+xz\right)=x^2+y^2+z^2\)

\(\Rightarrow2\left(xy+yz+xz\right)=0\)

\(\Rightarrow xy+yz+xz=0\Rightarrow\frac{xy+yz+xz}{xyz}=0\Rightarrow\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0\) 

\(\Rightarrow\frac{1}{x^3}+\frac{1}{y^3}+\frac{1}{z^3}=3.\frac{1}{x}.\frac{1}{y}.\frac{1}{z}=\frac{3}{xyz}\)

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