Gọi số lớn,số bé lần lượt là a,b
Ta có:\(\frac{a-b}{1}=\frac{a+b}{7}=\frac{ab}{24}\)
\(\Rightarrow\frac{a-b}{1}=\frac{a+b}{7}=\frac{ab}{24}=\frac{a-b+a+b+ab}{1+7+24}=\frac{2a+ab}{32}\)
\(\Rightarrow\frac{a\left(2+b\right)}{32}=\frac{ab}{24}\)
\(\Rightarrow a\left(2+b\right)\cdot24=ab\cdot32\)\(\Rightarrow24a\left(2+b\right)=32ab\)
\(\Rightarrow48a+2ab=32ab\)
\(\Rightarrow48a=32ab-2ab\)
\(\Rightarrow48a=32ab\)
\(\Rightarrow a=\frac{32}{48}ab\)
\(\Rightarrow a=\frac{2}{3}ab\)
\(\Rightarrow\frac{2}{3}b=1\)
\(\Rightarrow b=\frac{3}{2}\)
\(\Rightarrow\frac{a-\frac{3}{2}}{1}=\frac{a+\frac{3}{2}}{7}=\frac{a\cdot\frac{3}{2}}{24}\)
\(\Rightarrow a-\frac{3}{2}=\frac{a}{7}+\frac{\frac{3}{2}}{7}=a\cdot\frac{\frac{3}{2}}{24}\)
\(\Rightarrow a-\frac{3}{2}=\frac{a}{7}+\frac{3}{14}=a\cdot\frac{1}{16}\)
Ta có:\(a-\frac{3}{2}=\frac{a}{7}+\frac{3}{14}\)
\(\Rightarrow a-\frac{a}{7}=\frac{3}{14}+\frac{3}{2}\)
\(\Rightarrow\frac{6a}{7}=\frac{12}{7}\)
\(\Rightarrow6a=12\Rightarrow a=2\)
\(\Rightarrow a\cdot b=2\cdot\frac{3}{2}=3\)
