Question

Tìm x biết rằng:

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

Answer 1

Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:

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

                                                       \(=\frac{2\left(1+4y\right)}{2\left(3x+9\right)}=\frac{1+4y}{3x+9}\)

\(\Rightarrow\frac{1+4y}{24}=\frac{1+4y}{3x+9}\)

\(\Rightarrow3x+9=24\)

\(\Rightarrow x+3=24:3=8\)

\(\Rightarrow x=5\)

Answer 2

\(\frac{1+2y}{18}=\frac{2+4y}{36}=\frac{1+4y}{24}=\frac{2+4y-\left(1+4y\right)}{36-24}=\frac{1}{12}\)

\(\Rightarrow\frac{1+4y}{24}=\frac{1}{12}\Rightarrow4y+1=2\Rightarrow y=\frac{1}{4}\)

\(\Rightarrow\frac{1+6y}{6x}=\frac{1}{12}\Rightarrow x=2\cdot\left(1+6y\right)=2+12y=2+12\cdot\frac{1}{4}=5\)

Vậy x = 5.