Ta có :
\(a-b=1\)
\(\Rightarrow a=b+1\left(1\right)\)
\(A=a^3-b^3-ab\)
\(\Rightarrow A=\left(b+1\right)^3-b^3-\left(b+1\right)b\)
\(\Rightarrow A=b^3+3b^2+3b+1-b^3-b^2-b\)
\(\Rightarrow A=2b^2+2b+1\)
\(\Rightarrow A=2\left(b^2+b+\dfrac{1}{4}\right)-\dfrac{1}{2}+1\)
\(\Rightarrow A=2\left(b+\dfrac{1}{2}\right)^2+\dfrac{1}{2}\ge\dfrac{1}{2}\)
\(\Rightarrow A\left(min\right)=\dfrac{1}{2}\) khi \(a=\dfrac{1}{2};b=-\dfrac{1}{2}\)
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