\(A=\frac{1}{a}\)\(+\frac{1}{a}\)\(+\frac{1}{a}\)\(+\frac{1}{a}\)\(+\frac{1}{ab}\)\(\ge\frac{25}{4a+ab}\)\(=\frac{25}{a\left(b+4\right)}\)\(\ge\frac{25}{\frac{1}{4}\left(a+b+4\right)^2}\)\(=1\)
\(A_{min=1}\)\(khi\){ a = 5
b = 1
Lần đầu tiên làm toán lớp 8 , có gì sai sót mong bạn chỉ ra hộ mình
\(A=\frac{4}{a}+\frac{1}{ab}=\frac{1}{a}+\frac{1}{a}+\frac{1}{a}+\frac{1}{a}+\frac{1}{ab}\)
\(\Rightarrow A=\frac{1}{a}+\frac{1}{a}+\frac{1}{a}+\frac{1}{a}+\frac{1}{ab}\ge\frac{5^2}{4a+ab}=\frac{25}{a\left(4+b\right)}\)
\(=\frac{25}{\frac{1}{4}\left(a+b+4\right)^2}=\frac{25}{\frac{1}{4}.100}=1\)
Dấu "=" xảy ra \(\Leftrightarrow\frac{25}{a\left(b+4\right)}=1\Leftrightarrow a\left(b+4\right)=25\)
Mà a,b dương => MinA = 1 <=> a = 1 ; b = 5 ( tmđk )