Question

[Nguyễn Phan Hoàng]

Cần mng giúp ạ

Answer 1

[Nguyễn Minh Nghĩa]

\(T=\frac{\left(xy+z\right)\left(yz+x\right)\left(zx+y\right)}{\left(x+y\right)^2\left(y+z\right)^2\left(z+x\right)^2}\)

\(T=\frac{\left(xy+1-x-y\right)\left(yz+1-y-z\right)\left(zx+1-z-x\right)}{\left(x+y\right)^2\left(y+z\right)^2\left(z+x\right)^2}\)

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

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

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

\(T=\frac{\left(y+z\right)^2\left(x+z\right)^2\left(x+y\right)^2}{\left(x+y\right)^2\left(y+z\right)^2\left(z+x\right)^2}\)

\(T=1\). Vậy \(T\) không phụ thuộc vào \(x,y,z\).