Question

Tìm GTNN của biểu thức sau

Answer 1

a) \(A=4x^2-4x+9=\left(4x^2-4x+1\right)+8\)

\(=\left(2x-1\right)^2+8\ge8\)

\(minA=8\Leftrightarrow x=\dfrac{1}{2}\)

c) \(C=\left(x^2-4x+4\right)+\left(y^2+5y+\dfrac{25}{4}\right)-\dfrac{13}{4}\)

\(=\left(x-2\right)^2+\left(y+\dfrac{5}{2}\right)^2-\dfrac{13}{4}\ge-\dfrac{13}{4}\)

\(minC=-\dfrac{13}{4}\Leftrightarrow\) \(\left\{{}\begin{matrix}x=2\\y=-\dfrac{5}{2}\end{matrix}\right.\)