Giải thích các bước giải:
Ta có:
$\dfrac{y+z+t-nx}{x}=\dfrac{z+t+x-ny}{y}=\dfrac{t+x+y-nz}{z}=\dfrac{x+y+z-nt}{t}$
$\to \dfrac{y+z+t}{x}-n=\dfrac{z+t+x}{y}-n=\dfrac{t+x+y}{z}-n=\dfrac{x+y+z}{t}-n$
$\to \dfrac{y+z+t}{x}=\dfrac{z+t+x}{y}=\dfrac{t+x+y}{z}=\dfrac{x+y+z}{t}$
$\to \dfrac{y+z+t}{x}+1=\dfrac{z+t+x}{y}+1=\dfrac{t+x+y}{z}+1=\dfrac{x+y+z}{t}+1$
$\to \dfrac{y+z+t+x}{x}=\dfrac{z+t+x+y}{y}=\dfrac{t+x+y+z}{z}=\dfrac{x+y+z+t}{t}$
$\to \dfrac{x+y+z+t}{x}=\dfrac{x+y+z+t}{y}=\dfrac{x+y+z+t}{z}=\dfrac{x+y+z+t}{t}$
Nếu $x+y+z+t=0$
$\to t=-(x+y+z)$
$\to P=3x+2y-5z-(x+y+z)=2x+y-6z$
Nếu $x+y+z+t\ne 0$
$\to\dfrac1x=\dfrac1y=\dfrac1z=\dfrac1t$
$\to x=y=z=t$
$\to P=3x+2x-5x+x=x$
