\(A=\frac{8a^2+b}{4a}+b^2=2a+\frac{b}{4a}+b^2\)
\(\ge2a+\frac{1-a}{4a}+b^2=2a+\frac{1}{4a}-\frac{1}{4}+b^2\)
\(\ge a+\frac{1}{4a}-b+b^2+\frac{3}{4}\)
\(=\left(a+\frac{1}{4a}\right)+\left(b^2-b+\frac{1}{4}\right)+\frac{1}{2}\)
\(=\left(a+\frac{1}{4a}\right) +\left(b-\frac{1}{2}\right)^2+\frac{1}{2}\)
\(\ge1+\frac{1}{2}=\frac{3}{2}\)
Dấu ''='' xảy ra khi \(a=b=\frac{1}{2}\)