\(A=x^4+3x^2-2\)
\(=x^4+3x^2+\dfrac{9}{4}-\dfrac{17}{4}\)
\(=\left(x^2+\dfrac{3}{2}\right)^2-\dfrac{17}{4}\)
Ta có: \(\left(x^2+\dfrac{3}{2}\right)^2\ge0\forall x\Rightarrow\left(x^2+\dfrac{3}{2}\right)^2-\dfrac{17}{4}\ge-\dfrac{17}{4}\forall x\)
Dấu "=" xảy ra khi \(x^2+\dfrac{3}{2}=0\Leftrightarrow x^2=-\dfrac{3}{2}\)(vô lí)
Vậy A không có GTNN.
\(B=\left(3x+1\right)^2+\left(y-5\right)^2-15\)
Ta có: \(\left(3x+1\right)^2+\left(y-5\right)^2\ge0\forall x\Rightarrow\left(3x+1\right)^2+\left(y-5\right)^2-15\ge-15\forall x\)
Dấu "=" xảy ra khi \(3x+1=0\) và \(y-5=0\)
\(\Leftrightarrow x=-\dfrac{1}{3};y=5\)
Vậy MINB = -15 khi x = \(-\dfrac{1}{3}\) và y = 5.
