Question

a) 0,16:x = x:25

b) Cho \(\frac{3x-2y}{4}=\frac{2z-4x}{3}=\frac{4y-3z}{2}và2x+4y+5z=8\).Tính A= 2x+3y-z

Answer 1

\(\frac{4\left(3x-2y\right)}{16}=\frac{3\left(2z-4x\right)}{9}=\frac{2\left(4y-3z\right)}{4}=\frac{12x-8y+6z-12x+8y-6z}{16+9+4}=\frac{0}{29}=0\)

\(\Leftrightarrow3x-2y=0\Leftrightarrow\frac{x}{2}=\frac{y}{3}\)

\(\Leftrightarrow2z-4x=0\Leftrightarrow\frac{x}{2}=\frac{z}{4}\)

\(\Leftrightarrow\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\)

\(\Leftrightarrow\frac{x}{2}=\frac{y}{3}=\frac{z}{4}=\frac{2x+4y+5z}{4+12+20}=\frac{8}{36}=\frac{2}{9}=\frac{2x+3y-z}{4+12-4}\)=> A= 2x+3y -z = 12.2/9  =8/3