Question

cho 2(x+y)=5(y+z)=3(z+x) chứng mình rằng x-y/4=y-z/5

Answer 1

Lời giải:

$2(x+y)=5(y+z)=3(z+x)$

$\Rightarrow \frac{x+y}{15}=\frac{y+z}{6}=\frac{z+x}{10}$

Đặt $\frac{x+y}{15}=\frac{y+z}{6}=\frac{z+x}{10}=t$

$\Rightarrow x+y=15t; y+z=6t; z+x=10t$

$\Rightarrow 2(x+y+z)=x+y+y+z+z+x=15t+6t+10t=31t$

$\Rightarrow x+y+z=15,5t$

$z=(x+y+z)-(x+y)=15,5t-15t=0,5t$

$x=(x+y+z)-(y+z)=15,5t-6t=9,5t$

$y=(x+y+z)-(x+z)=15,5t-10t=5,5t$

Suy ra:

$\frac{x-y}{4}=\frac{9,5t-5,5t}{4}=t$

$\frac{y-z}{5}=\frac{5,5t-0,5t}{5}=t$

$\Rightarrow \frac{x-y}{4}=\frac{y-z}{5}$