Question

Tìm các số x, y, z, biết rằng: a. \(\frac{1+4y}{13}=\frac{1+6y}{19}=\frac{1+8y}{5x}\)

b.\(\frac{2x+1}{5}=\frac{y-2}{7}=\frac{2x+3y-1}{6x}\)

c.\(\frac{y+z+1}{x}=\frac{x+z+2}{y}=\frac{y+x-3}{z}=\frac{1}{x+y+z}\)

Answer 1

a) Ta có: \(\frac{1+4y}{13}=\frac{1+6y}{19}.\)

\(\Rightarrow\left(1+4y\right).19=\left(1+6y\right).13\)

\(\Rightarrow19+76y=13+78y\)

\(\Rightarrow19-13=78y-76y\)

\(\Rightarrow6=2y\)

\(\Rightarrow y=6:2\)

\(\Rightarrow y=3.\)

Thay \(y=3\) vào đề bài ta được:

\(\frac{1+4.3}{13}=\frac{1+8.3}{5x}\)

\(\Rightarrow\frac{1+12}{13}=\frac{1+24}{5x}.\)

\(\Rightarrow\frac{13}{13}=\frac{25}{5x}\)

\(\Rightarrow1=\frac{25}{5x}\)

\(\Rightarrow5x=25:1\)

\(\Rightarrow5x=25\)

\(\Rightarrow x=25:5\)

\(\Rightarrow x=5\)

Vậy \(\left(x;y\right)=\left(5;3\right).\)

Chúc bạn học tốt!