Question

Tìm GTNN A=/x-1/+/2y-3/+1001

Answer 1

\(A\ge1001\forall x,y\)

Dấu '=' xảy ra khi x=1 và y=3/2

Answer 2

Vì |x-1|≥0\(\forall x\)

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

|2y-3|≥0\(\forall y\)

Dấu "=" xảy ra \(\Leftrightarrow y=\dfrac{3}{2}\)

\(\Rightarrow A=\left|x-1\right|+\left|2y-3\right|+1001\ge1001\forall x,y\)

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

Vậy \(A_{min}=1001\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=\dfrac{3}{2}\end{matrix}\right.\)