Question

cho 

chứng minh rqngf biểu thức 

Answer 1

\(\dfrac{x}{y+z+t}=\dfrac{y}{z+t+x}=\dfrac{z}{t+x+y}=\dfrac{t}{x+y+z}\)

\(\Rightarrow\dfrac{y+z+t}{x}=\dfrac{z+t+x}{y}=\dfrac{t+x+y}{z}=\dfrac{x+y+z}{t}\)

\(\Rightarrow\dfrac{y+z+t}{x}+1=\dfrac{z+t+x}{y}+1=\dfrac{t+x+y}{z}+1=\dfrac{x+y+z}{t}+1\)

\(\Rightarrow\dfrac{x+y+z+t}{x}=\dfrac{z+t+x+y}{y}=\dfrac{t+x+y+z}{z}=\dfrac{x+y+z+t}{t}\)

Nếu \(x+y+z+t=0\Rightarrow P=-4\)

Nếu \(x+y+z+t\ne0\Rightarrow x=y=z=t\Rightarrow P=4\)

Vậy P nguyên