\(A=x^2+20y^2+8xy-4y+2015\)

\(=\left(x^2+8xy+16y^2\right)+\left(4y^2-4y+1\right)+2014\)

\(=\left(x+4y\right)^2+\left(2y-1\right)^2+2014\ge2014\forall x\)

Dấu "=" xảy ra khi:

\(\hept{\begin{cases}x+4y=0\\2y-1=0\end{cases}\Rightarrow}\hept{\begin{cases}x=-2\\y=\frac{1}{2}\end{cases}}\)

Vậy GTNN của A là 2014 khi \(x=-2,y=\frac{1}{2}\)

\(B=\frac{x^2-2x+2016}{x^2}\)

\(=\frac{2016x^2-2.x.2016+2016^2}{2016x^2}\)

\(=\frac{\left(x^2-2.x.2016+2016^2\right)+2015x^2}{2016x^2}\)

\(=\frac{\left(x-2016\right)^2+2015x^2}{2016x^2}=\frac{\left(x-2016\right)^2}{2016x^2}+\frac{2015}{2016}\ge\frac{2015}{2016}\forall x\)

Dấu "=" xảy ra khi: \(x-2016=0\Rightarrow x=2016\)

Vậy GTNN của B là \(\frac{2015}{2016}\)khi x = 2016

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(x-y+4)² - (2x+y-1)²

= (x-y+4 + 2x+y-1 ) . (x-y+4 - 2x+y-1)

1. \(4x^2-17xy+13y^2=4x^2-4xy-13xy+13y^2=4x\left(x-y\right)-13y\left(x-y\right)=\left(x-y\right)\left(4x-13y\right)\)

2. \(2x\left(x-5\right)-x\left(3+2x\right)=26\Leftrightarrow2x^2-10x-3x-2x^2=26\Leftrightarrow-13x=26\Leftrightarrow x=-2\)

3. \(A=\left(2a-3b\right)^2+2\left(2a-3b\right)\left(3a-2b\right)+\left(2b-3a\right)^2\)

\(\Leftrightarrow\left(2a-3b\right)^2-2\left(2a-3b\right)\left(2b-3a\right)+\left(2b-3a\right)^2=\left(2a-3b-2b+3a\right)^2=\left(5a-5b\right)^2\)

\(=25\left(a-b\right)^2=25\cdot100=2500\)

\(a,ax+by+ay+bx=\left(ax+ay\right)+\left(by+bx\right)=a\left(x+y\right)+b\left(x+y\right)=\left(a+b\right)\left(x+y\right)\)

\(b,x^2y+xy+x+1=xy\left(x+1\right)+\left(x+1\right)=\left(xy+1\right)\left(x+1\right)\)

\(c,x^2-ax-bx+ab=x\left(x-a\right)-b\left(x-a\right)=\left(x-b\right)\left(x-2\right)\)

\(d,x^2y+xy^2-x-y=xy\left(x+y\right)-\left(x+y\right)=\left(xy-1\right)\left(x+y\right)\)

\(e,a\left(x^2+y\right)-b\left(x^2+y\right)=\left(a-b\right)\left(x^2+y\right)\)

\(f,x\left(a-2\right)-a\left(a-2\right)=\left(x-a\right)\left(a-2\right)\)