A = x² - 2xy + y² + 4x² + 6x + 9 + 4y² - 6x + 9 -18

A = (x-y)²+(2x+1)²+(2y-1)² - 18 ≥ -18

vật min của A là -18 khi x = -\(\frac{1}{2}\); y = \(\frac{1}{2}\)

eyyy man

(109-x)/91+(107-x)/93+(105-x)/95+(103-x)/97=-4

[(109-x)/91 +1]+[(107-x)/93 +1]+[(105-x)/95 +1]+[(103-x)/97 +1]-4=-4

(109+91-x)/91+(107+93-x)/93+(105+95-x)/95+(103+97-x)/97=-4+4

(200-x)/91+(200-x)/93+(200-x)/95+(200-x)/97=0

(200-x)(1/91+1/93+1/95+1/97)=0

Ma : 1/91+1/93+1/95+1/97\(\ne\)0

=>200-x=0

=>x=200

a, \(5y^2-5x^2+6x+6y=5\left(y-x\right)\left(x+y\right)+6\left(x+y\right)\)

\(=\left(x+y\right)\left(5y-5x+6\right)\)

b, \(12x^2+19x+7=12x^2+12x+7x+7\)

\(=12x\left(x+1\right)+7\left(x+1\right)=\left(12x+7\right)\left(x+1\right)\)

5y² - 5x² + 6x + 6y 

= 5(y² - x²) + 6(x + y) 

= 5(y - x)(x + y) + 6(x + y) 

= (x + y)(5y - 5x + 6) 

b) 12x² + 19x + 7 

= 12x² + 12x + 7x + 7 

= 12x(x + 1) + 7(x + 1) 

= (x + 1)(12x + 7) 

gọi biểu thức trên là A.

Ta có: \(A=x^2-2xy+2y^2-6y+9\)

\(\Rightarrow A=x^2-2xy+y^2+y^2-6y+9\)

\(\Rightarrow A=\left(x^2-2xy+y^2\right)+\left(y^2-6y+9\right)\)

 \(A=\left(x-y\right)^2+\left(y-3\right)^2\)

Nhận xét: \(\left(x+y\right)^2\ge0\forall x,y\)

                 \(\left(y-3\right)^2\ge0\forall y\)

\(\Rightarrow\left(x+y\right)^2+\left(y-3\right)^2\ge0\forall x,y\)

Vậy \(minA=0\) khi \(y-3=0\Rightarrow y=3\)

                                       \(x-y=0\Rightarrow x-3=0\Rightarrow x=3\)

KL: Vậy \(minA=0\) khi \(x=3;y=3\)

Đặt \(A=x^2-2xy+2y^2-6y+9=\left(x^2-2xy+y^2\right)+\left(y^2-6y+9\right)=\left(x-y\right)^2+\left(y-3\right)^2\)

Vì \(\left(x-y\right)^2\ge0;\left(y-3\right)^2\ge0\Rightarrow A=\left(x-y\right)^2+\left(y-3\right)^2\ge0\)

Dấu "=" xảy ra \(\Leftrightarrow\hept{\begin{cases}x-y=0\\y-3=0\end{cases}\Leftrightarrow x=y=3}\)

Vậy Amin = 0 khi x = y = 3

b)x²+2xy+y²-16=(x+y)²-4²=(x+y+4)(x+y-4)

c)3x²+5x-3xy-5y=x(3x+5)-y(3x+5)=(3x+5)(x-y)

d)4x²-6x³y-2x²+8x=2x(2x-3x²y-x+4)

e)x²-4-2xy+y²=(x²-2xy+y²)-4=(x-y)²-2²=(x-y-2)(x-y+2)

k)x²-y²-z²-2yz=x²-(y+z)²=(x-y-z)(x+y+z)

m)6xy+5x-5y-3x²-3y²=3(x²-2xy+y²)+5(x-y)=3(x-y)²+5(x-y)=(x-y)(3x-3y+5)

b. (x^2+2xy+y^2)-16 =(x+y)^2-16=(x+y+4)(x+y-4)