Question

Tìm x; y

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

Answer 1

Theo định nghĩa hai phân số bằng nhau ta có:

\(\dfrac{1+2y}{18}=\dfrac{1+4y}{24}\)

khi và chỉ khi: \(\left(1+2y\right).24=\left(1+4y\right).18\) \(\Rightarrow24+48y=18+72y\)

\(\Rightarrow72y-48y=24-18\)

\(\Rightarrow24y=6\) \(\Rightarrow y=\dfrac{1}{4}\) Lại có: \(\dfrac{1+4y}{24}=\dfrac{1+6y}{6x}\) \(\Rightarrow\dfrac{1+4\cdot\dfrac{1}{4}}{24}=\dfrac{1+6\cdot\dfrac{1}{4}}{6x}\) \(\Rightarrow\dfrac{1}{12}=\dfrac{\dfrac{5}{2}}{6x}\) \(\Rightarrow6x.1=12\cdot\dfrac{5}{2}\) \(\Rightarrow x=30:6=5\) Vậy x=5;y=\(\dfrac{1}{4}\)