Question

Tìm x,y,z biết

\(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\)=3và \(\frac{1}{xY}+\frac{1}{YZ}+\frac{1}{zX}\) =3

Answer 1

bài này mình nghĩ của lớp 8

Answer 2

Ta có: \(\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)^2=3^2=9\Leftrightarrow\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}+2\left(\frac{1}{xy}+\frac{1}{yz}+\frac{1}{zx}\right)=9\)

\(\Rightarrow\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=3\)\(\Rightarrow\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}-\frac{1}{x}-\frac{1}{y}-\frac{1}{z}=0\)

\(\Leftrightarrow\left(\frac{1}{x}-1\right)^2+\left(\frac{1}{y}-1\right)^2+\left(\frac{1}{z}-1\right)^2=0\)\(\Leftrightarrow x=y=z=1\)