\(\Rightarrow\left(\frac{x}{y+z}+\frac{y}{z+x}+\frac{z}{x+y}\right).\left(x+y+z\right)=x+y+z\)
\(\Rightarrow\frac{x^2+x\left(z+x\right)}{y+z}+\frac{y^2+y\left(x+z\right)}{x+z}+\frac{z^2+z\left(x+y\right)}{x+y}=x+y+z\)
\(\Rightarrow\frac{x^2}{y+z}+x+\frac{y^2}{x+z}+y+\frac{z^2}{x+y}+z=x+y+z\)
\(\Rightarrow\frac{x^2}{y+z}+\frac{y^2}{x+z}+\frac{z^2}{x+y}=0\)
Cho x+y+z=7. Biết \frac{x}{y+z} +\frac{y}{x+z} +\frac{z}{x+y} = 3. Tính \frac{x^{2}}{y+z} +\frac{y^{2}}{x+z} +\frac{z^{2}}{x+y}
Tính:a) \(A=\frac{2}{x-y}+\frac{2}{y-z}+\frac{2}{z-x}+\frac{\left(x-y\right)^2+\left(y-z\right)^2+\left(z-x\right)^2}{\left(x-y\right)\left(y-z\right)\left(z-x\right)}\)
b) Cho \(\frac{x}{y+z}+\frac{y}{z+x}+\frac{z}{x+y}=1\) . Tính \(A=\frac{x^2}{y+z}+\frac{y^2}{z+x}+\frac{z^2}{x+y}\)
CHo \(\frac{x}{y+z}+\frac{y}{z+x}+\frac{z}{x+y}=1\)
Tính : \(A=\frac{x^2}{y+z}+\frac{y^2}{x+z}+\frac{z^2}{x+y}\)
Cho \(x+y+z\ne0,\frac{x^2}{y+z}+\frac{y^2}{z+x}+\frac{z^2}{x+y}=0\)
Tính \(P=\frac{x}{y+z}+\frac{y}{z+x}+\frac{z}{x+y}\)
Cho \(\frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{x+y}=1\).Tính giá trị biểu thúc \(M=2019+\frac{x^2}{y+z}+\frac{y^2}{x+z}+\frac{z^2}{x+y}\)
Cho: \(\frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{x+y}=1\)
Tính: \(2020+\frac{x^2}{y+z}+\frac{y^2}{x+z}+\frac{z^2}{x+y}\)
\(x+y+z=1,\frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{x+y}=1\)
tính giá trị của biểu thức A=\(\frac{x^2}{y+z}+\frac{y^2}{x+z}+\frac{z^2}{x+y}\)
Cho biết \(\frac{x^2}{x+y}+\frac{y^2}{y+z}+\frac{z^2}{z+x}=2017.\)Tính \(\frac{y^2}{x+y}+\frac{z^2}{y+z}+\frac{x^2}{z+x}.\)
Cho\(\frac{x^2}{x+y}+\frac{y^2}{y+z}+\frac{z^2}{z+x}=2009\)
Tính \(\frac{y^2}{x+y}+\frac{z^2}{y+z}+\frac{x^2}{z+x}\)
