Theo bài ra ta có: \(\dfrac{a+b}{7}=\dfrac{a-b}{1}=\dfrac{ab}{24}\)
Áp dụng tính chất dãy tỉ số bằng nhau
\(\dfrac{a+b}{7}=\dfrac{a-b}{1}=\dfrac{ab}{24}=\dfrac{a+b+a-b}{7+1}=\dfrac{2a}{8}=\dfrac{a}{4}\)
\(\Rightarrow\dfrac{ab}{24}=\dfrac{a}{4}\Rightarrow\dfrac{ab}{24}=\dfrac{6a}{24}\Rightarrow ab=6a\Rightarrow b=6\)
Thay b = 6 vào \(\dfrac{a+b}{7}=\dfrac{a-b}{1}\) ta được:
\(\dfrac{a+18}{7}=\dfrac{a-18}{1}\)
\(\Rightarrow\left(a+18\right).1=7.\left(a-18\right)\)
\(\Rightarrow a+18=7a-126\)
\(\Rightarrow a-7a=-126-18\)
\(\Rightarrow-6a=-144\)
\(\Rightarrow6a=144\)
\(\Rightarrow a=144:6\)
\(\Rightarrow a=24\)
Vậy a = 24, b = 18
Theo bài ra ta có: \(\dfrac{a+b}{7}=\dfrac{a-b}{1}=\dfrac{ab}{24}\)
Áp dụng tính chất dãy tỉ số bằng nhau
\(\dfrac{a+b}{7}=\dfrac{a-b}{1}=\dfrac{ab}{24}=\dfrac{a+b+a-b}{7+1}=\dfrac{2a}{8}=\dfrac{a}{4}\) \(\Rightarrow\dfrac{ab}{24}=\dfrac{a}{4}\Rightarrow\dfrac{ab}{24}=\dfrac{6a}{24}\Rightarrow ab=6a\Rightarrow b=6\)
Thay b = 6 vào \(\dfrac{a+b}{7}=\dfrac{a-b}{1}\) ta được:
\(\dfrac{a+6}{7}=\dfrac{a-6}{1}\)
\(\Rightarrow\left(a+6\right).1=7.\left(a-6\right)\)
\(\Rightarrow a+6=7a-42\)
\(\Rightarrow a-7a=-42-6\)
\(\Rightarrow-6a=-48\)
\(\Rightarrow6a=48\)
\(\Rightarrow a=48:6\)
\(\Rightarrow a=8\)
Vậy a = 8, b = 6
