a.

\(F=\dfrac{a}{b+2}\Rightarrow F.b+2F=a\)

\(\Rightarrow2F=a-F.b\)

\(\Rightarrow4F^2=\left(a-F.b\right)^2\le\left(a^2+b^2\right)\left(1^2+F^2\right)=F^2+1\)

\(\Rightarrow3F^2\le1\)

\(\Rightarrow-\dfrac{1}{\sqrt{3}}\le F\le\dfrac{1}{\sqrt{3}}\)

Dấu "=" lần lượt xảy ra tại \(\left(a;b\right)=\left(-\dfrac{\sqrt{3}}{2};-\dfrac{1}{2}\right)\) và \(\left(\dfrac{\sqrt{3}}{2};-\dfrac{1}{2}\right)\)

b. Đặt \(\left\{{}\begin{matrix}a+b=x\\a-2b=y\end{matrix}\right.\) quay về câu a

a, \(\left(a^2+b^2-2ab+2a-2b+1\right)+\left(b^2-2b+1\right)=0\)

=> \(\left(a-b+1\right)^2+\left(b-1\right)^2=0\)

Mà \(\left(a-b+1\right)^2\ge0,\left(b-1\right)^2\ge0\)

=> \(\hept{\begin{cases}a-b+1=0\\b=1\end{cases}\Rightarrow\hept{\begin{cases}a=0\\b=1\end{cases}}}\)

b,Tương tự 

\(\left(a-2b+1\right)^2+\left(b-1\right)^2=0\)

=>\(\hept{\begin{cases}a=1\\b=1\end{cases}}\)

Đừng dùng đạo hàm hay gì nhá

Chắc câu a là \(2a^2\) ...

\(A=\left(a^2+b^2+2ab-4a-4b+4\right)+\left(a^2-2a+1\right)+\left(b^2-2b+1\right)+4014\)

\(A=\left(a+b-2\right)^2+\left(a-1\right)^2+\left(b-1\right)^2+4014\ge4014\)

\(A_{min}=4014\) khi \(a=b=1\)

\(B=\left(x^2-7x\right)\left(x^2-7x+12\right)=\left(x^2-7x\right)^2+12\left(x^2-7x\right)\)

\(B=\left(x^2-7x+6\right)^2-36\ge-36\)

\(B_{min}=-36\) khi \(\left[{}\begin{matrix}x=1\\x=6\end{matrix}\right.\)