Question

[ha nguyen thi]

tìm gtnn ; c = 2020 l 2x - 3 l  + 2021 l 3y + 1 l  + 2021

Answer 1

[𝓓𝓾𝔂 𝓐𝓷𝓱]

\(C\ge2021\)

Dấu bằng xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}2x-3=0\\3y+1=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3}{2}\\y=-\dfrac{1}{3}\end{matrix}\right.\)

  Vậy \(C_{Min}=2021\) khi \(x=\dfrac{3}{2}\) và \(y=-\dfrac{1}{3}\)

Answer 2

[Shiba Inu]

Vì |2x - 3| \(\ge\) 0, \(\forall\)x     ;    |3y + 1| \(\ge\) 0,\(\forall\)y

\(\Rightarrow\) C = 2020|2x - 3| + 2021|3y + 1| + 2021 \(\ge\) 2021, \(\forall\)x,y

Dấu " = " xảy ra khi và chỉ khi :

\(\left\{{}\begin{matrix}\left|2x-3\right|=0\\\left|3y+1\right|=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\dfrac{3}{2}\\y=-\dfrac{1}{3}\end{matrix}\right.\)

Vậy C_min = 2021 với \(x=\dfrac{3}{2};y=-\dfrac{1}{3}\)