Question

Tìm GTNN

a) B=x^2+y^2-x+4y+10

b) C=2x^2-6x

Answer 1

\(B=x^2+y^2-x+4y+10\)

\(=\left(x^2-x+\frac{1}{4}\right)+\left(y^2+4y+4\right)+\frac{23}{4}\)

\(=\left(x-\frac{1}{2}\right)^2+\left(y+2\right)^2+\frac{23}{4}\ge\frac{23}{4}\forall x\)

=> Min B = 23/4 tại \(\hept{\begin{cases}x=\frac{1}{2}\\y=-2\end{cases}}\)

Answer 2

\(C=2x^2-6x\)

\(=2x^2-6x+\frac{9}{2}-\frac{9}{2}\)

\(=2\left(x^2-3x+\frac{9}{4}\right)-\frac{9}{2}\)

\(=2\left(x-\frac{3}{2}\right)^2-\frac{9}{2}\ge-\frac{9}{2}\forall x\)

=> Min C = -9/2 tại \(x=\frac{3}{2}\)