Question

Answer 1

\(a,A=3\left|2x-1\right|-5\ge-5\\ A_{min}=-5\Leftrightarrow x=\dfrac{1}{2}\\ b,B=\left|x-1\right|+\left(y+2\right)^2+2021\ge2021\\ B_{min}=2021\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-2\end{matrix}\right.\)

Answer 2

a) \(A=3\left|2x-1\right|-5\ge-5\)

\(minA=-5\Leftrightarrow x=\dfrac{1}{2}\)

b) \(B=\left|x-1\right|+\left(y+2\right)^2+2021\ge2021\)

\(minB=2021\Leftrightarrow\)\(\left\{{}\begin{matrix}x=1\\y=-2\end{matrix}\right.\)

 

Answer 3

\(\left|2x-1\right|\ge0\)

dấu "=" xảy ra \(\Leftrightarrow x=\dfrac{1}{2}\)

\(\Rightarrow A=3\left|2x-1\right|-5\ge-5\)

dấu "=" xảy ra \(\Leftrightarrow x=\dfrac{1}{2}\)

Vậy \(A_{min}=-5\Leftrightarrow x=\dfrac{1}{2}\)

b) \(\left|x-1\right|\ge0\)

dấu "=" xảy ra \(\Leftrightarrow x=1\)

\(\left(y+2\right)^2\ge0\)

dấu "=" xảy ra \(\Leftrightarrow y=-2\)

\(\Rightarrow B=\left|x-1\right|+\left(y+2\right)^2\ge2021\)

dấu "=" xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-2\end{matrix}\right.\)

Vậy \(B_{min}=2021\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-2\end{matrix}\right.\)