Question

cho 3 số x,y,z thỏa mãn \(\frac{x}{1998}=\frac{y}{1999}=\frac{z}{2000}\)

CMR (x-z)³=8(x-y)²(y-z)

Answer 1

\(\frac{x}{1998}=\frac{y}{1999}=\frac{z}{2000}\)

\(\Rightarrow\frac{x-z}{1998-2000}=\frac{x-y}{1998-1999}=\frac{y-z}{1999-2000}\)

\(\Rightarrow\frac{x-z}{-2}=\frac{x-y}{-1}=\frac{y-z}{-1}\)

\(\Rightarrow\left(\frac{x-z}{-2}\right)^3=\left(\frac{x-y}{-1}\right)^2.\left(\frac{y-z}{-1}\right)\)

\(\Rightarrow\frac{\left(x-z\right)^3}{\left(-2\right)^3}=\frac{\left(x-y\right)^2}{\left(-1\right)^2}.\frac{\left(y-z\right)}{-1}\)

\(\Rightarrow\left(x-z\right)^3=8.\left(x-y\right)^2.\left(y-z\right)\)