Question

[Dương Ngọc]

a.tìm x biết:

1+2y/18 = 1+4y/24 = 1 +6y/6x

b. tìm x, y, z biết

y+z+1/x = x+z+2/y = 1/x+y+z = x+y+z/z

Answer 1

[Vũ Minh Tuấn]

a)

Ta có \(\frac{1+2y}{18}=\frac{1+4y}{24}.\)

\(\Rightarrow\left(1+2y\right).24=\left(1+4y\right).18\)

\(\Rightarrow24+48y=18+72y\)

\(\Rightarrow24-18=72y-48y\)

\(\Rightarrow6=24y\)

\(\Rightarrow y=6:24\)

\(\Rightarrow y=\frac{1}{4}.\)

+ Thay \(y=\frac{1}{4}\) vào đề bài ta được:

\(\frac{1+2.\frac{1}{4}}{18}=\frac{1+4.\frac{1}{4}}{24}=\frac{1+6.\frac{1}{4}}{6x}\)

\(\Rightarrow\frac{1}{12}=\frac{\frac{5}{2}}{6x}\)

\(\Rightarrow12.\frac{5}{2}=6x\)

\(\Rightarrow30=6x\)

\(\Rightarrow x=30:6\)

\(\Rightarrow x=5\)

Vậy \(\left(x;y\right)=\left(5;\frac{1}{4}\right).\)

Chúc bạn học tốt!