\(\dfrac{a+b}{10}=\dfrac{a-b}{2}=\dfrac{ab}{24}\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có:
\(\dfrac{ab}{24}=\dfrac{a+b}{10}=\dfrac{a-b}{2}=\dfrac{a+b+a-b}{10+2}=\dfrac{a+b-\left(a-b\right)}{10-2}\\ \Leftrightarrow\dfrac{ab}{24}=\dfrac{a+b}{10}=\dfrac{a-b}{2}=\dfrac{2a}{12}=\dfrac{a}{6}=\dfrac{2b}{8}=\dfrac{b}{4}\\ \dfrac{ab}{24}=\dfrac{a}{6}=\dfrac{b}{4}=k\\ \Rightarrow a=6k;b=4k;ab=24k\\ ab=24k\\ \Leftrightarrow6k.4k=24k^2=24k\\ \Leftrightarrow k^2=k\\ \Leftrightarrow k^2-k=0\\ \Leftrightarrow k\left(k-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}k=0\\k=1\end{matrix}\right.\\ k=0\Rightarrow\left\{{}\begin{matrix}a=6k=6.0=0\\b=4k=4.0=0\end{matrix}\right.\\ k=1\Rightarrow\left\{{}\begin{matrix}a=6k=6.1=6\\b=4k=4.1=4\end{matrix}\right.\)
