Vì \(\frac{ab}{2}=8\cdot\frac{a}{b}\)nên\(\Leftrightarrow a\cdot\frac{b}{2}=8\cdot\frac{a}{b}\)
\(\Leftrightarrow\frac{\left(\frac{ab}{2}\right)}{\left(\frac{a}{b}\right)}=8\Leftrightarrow\frac{ab}{2}\cdot\frac{b}{a}=8\Leftrightarrow\frac{ab^2}{2a}=8\)
\(\Leftrightarrow\frac{b^2}{2}=8\Leftrightarrow b^2=8\cdot2=16\Leftrightarrow b=\sqrt{16}=4\)
Vì \(a+\frac{b}{2}=\frac{ab}{2}\)(1)mà \(b=4\) nên thay b vào biểu thức (1)được:
\(a+\frac{4}{2}=\frac{a4}{2}\Leftrightarrow a+2=a\cdot2\)
\(\Leftrightarrow2=a\)
Vậy \(a=2;b=4\)để thỏa mãn \(a+\frac{b}{2}=\frac{ab}{2}=8\cdot\frac{a}{b}\)
