Question

tìm GTNN:

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

b)C=x^2+y^2-xy+4x-5y+1018

Answer 1

\(C=\left(x^2+\dfrac{y^2}{4}+4-xy+4x-2y\right)+\dfrac{3}{4}\left(y^2-4y+4\right)+1011\)

\(=\left(x-\dfrac{y}{2}+2\right)^2+\dfrac{3}{4}\left(y-2\right)^2+1011\ge1011\)

Dấu "=" xảy ra khi \(\left(x;y\right)=\left(-1;2\right)\)

Answer 2

a) Ta có: \(B=x^2+4y^2+4x-4y\)

\(=\left(x^2+4x+4\right)+\left(4y^2-4y+1\right)-5\)

\(=\left(x+2\right)^2+\left(2y-1\right)^2-5\ge-5\forall x,y\)

Dấu '=' xảy ra khi \(\left(x,y\right)=\left(-2;\dfrac{1}{2}\right)\)