Question

Tìm GTNN của biểu thức A=|3x-1|+\(^{\left(2x-1\right)^2}\)+2021

 

 

Answer 1

Ta có:
\(\left|3x-1\right|\ge0\)

Dấu "=" xảy ra \(\Leftrightarrow x=\dfrac{1}{3}\)

\(\left(2y-1\right)^2\ge0\)

Dấu "=" xảy ra \(\Leftrightarrow y=\dfrac{1}{2}\)

\(\Rightarrow\left|3x-1\right|+\left(2y-1\right)^2+2021\ge0\)

Dấu "=" xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{3}\\y=\dfrac{1}{2}\end{matrix}\right.\)

Vậy \(A_{min}=2021\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{3}\\y=\dfrac{1}{2}\end{matrix}\right.\)