Question

Cho x^2 = yz Chứng minh rằng x + y / x - y = z + x / z - x

giúp mình nha 

Answer 1

Ta co : 

\(x^2=\frac{x}{y};yz=\frac{z}{x}\Rightarrow x^2=yz=\frac{x}{y}=\frac{z}{x}\)

Dat : \(\frac{x}{y}=\frac{z}{x}=k\)

x=yk

z=xk

\(\frac{x+y}{x-y}=\frac{yk+y}{yk-y}=\frac{y.\left(k+1\right)}{y.\left(k-1\right)}=\frac{k+1}{k-1}\)        (1)

\(\frac{z+x}{z-x}=\frac{xk+x}{xk-x}=\frac{x.\left(k+1\right)}{x.\left(k-1\right)}=\frac{k+1}{k-1}\)       (2)

​               Vậy  từ (1) và (2) suy ra \(\frac{x+y}{x-y}=\frac{z+x}{z-x}\)