Question

Tìm GTNN của các biểu thức sau:

a) A= 3/2x-1/-5

b) P= \(^{x^2}\)+3/y-2/-1

Answer 1

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

Ta thấy : \(\left|2x-1\right|\ge0\)

\(\Leftrightarrow3\left|2x-1\right|-5\ge-5\)

Dấu " = " xảy ra :

\(\Leftrightarrow2x-1=0\)

\(\Leftrightarrow x=\frac{1}{2}\)

Vậy \(Min_A=-5\Leftrightarrow x=\frac{1}{2}\)

b) \(P=x^2+3\left|y-2\right|-1\)

Ta thấy : \(x^2\ge0\)

\(\left|y-2\right|\ge0\)

\(\Leftrightarrow x^2+3\left|y-2\right|-1\ge-1\)

Dấu " = " xảy ra :

\(\Leftrightarrow\left\{{}\begin{matrix}x^2=0\\y-2=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=0\\y=2\end{matrix}\right.\)

Vậy \(Min_P=-1\Leftrightarrow\left(x;y\right)=\left(0;2\right)\)