\(x^2+xy+y^2-2x-3y+2015=\frac{x^2}{2}+xy+\frac{y^2}{2}+\frac{x^2}{2}-2x+2+\frac{y^2}{2}-3y+\frac{9}{2}+2008\frac{1}{2}\)

\(\Leftrightarrow P=\frac{1}{2}\left(x+y\right)^2+\frac{1}{2}\left(2-x\right)^2+\frac{1}{2}\left(3-y\right)^2+2008,5\)

Xét : \(\left(x+y\right)^2+\left(2-x\right)^2+\left(3-y\right)^2\ge\frac{\left(x+y+2-x+3-y\right)^2}{3}=\frac{25}{3}\)(BĐT Bunia )

\(\Rightarrow P\ge\frac{25}{6}+2008,5\)

dấu bằng xảy ra khi \(x+y=2-x=3-y\Leftrightarrow\hept{\begin{cases}x=\frac{1}{3}\\y=\frac{4}{3}\end{cases}}\)

TL:

x=\(\frac{1}{3}\)

y=\(\frac{4}{3}\)

-HT-

Câu hỏi của vũ nguyễn gia linh - Toán lớp 8 - Học toán với OnlineMath

Bn kham khảo nhé ! 

a, \(3x\left(x-2\right)-2x+4=3x\left(x-2\right)-2\left(x-2\right)=\left(3x-2\right)\left(x-2\right)\)

b, \(x^2+2xy+y^2-9z^2=\left(x+y\right)^2-\left(3z\right)^2=\left(x+y-3z\right)\left(x+y+3z\right)\)

c, \(x^2+xy-3x-3y=x\left(x+y\right)-3\left(x+y\right)=\left(x-3\right)\left(x+y\right)\)

d, \(x^2-4xy-9+4y^2=\left(x+2y\right)^2-3^2=\left(x+2y-3\right)\left(x+2y+3\right)\)

e, \(x^2-5x-xy+5y=x\left(x-y\right)-5\left(x-y\right)=\left(x-5\right)\left(x-y\right)\)

g, \(x^2+2xy-9+y^2=\left(x+y\right)^2-3^2=\left(x+y-3\right)\left(x+y+3\right)\)

h, \(7x\left(x-2021\right)-x+2021=7x\left(x-2021\right)-\left(x-2021\right)=\left(7x-1\right)\left(x-2021\right)\)

i, \(\left(3x+1\right)^2-\left(2x-3\right)^2=\left(3x+1-2x+3\right)\left(3x+1+2x-3\right)=\left(x+4\right)\left(5x-2\right)\)

c) \(3x\left(x-2\right)-2x+4\)

\(3x\left(x-2\right)-2\left(x-2\right)\)

\(\left(x-2\right)\left(3x-2\right)\)

d) \(x^2+2xy+y^2-9z^2\)

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

\(\left(x-y-3z\right)\left(x-y+3z\right)\)

e)\(x^2+xy-3x-3y\)

\(x\left(x+y\right)-3\left(x+y\right)\)

\(\left(x+y\right)\left(x-3\right)\)

f) \(x^2-4xy-9+4y^2\)

\(\left(x-2y\right)^2-3^2\)

\(\left(x-2y-3\right)\left(x-2y+3\right)\)

g) \(x^2-5x-xy+5y\)

\(x\left(x-5\right)-y\left(x-5\right)\)

\(\left(x-5\right)\left(x-y\right)\)

h) \(x^2+2xy+y^2-9\)

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

\(\left(x-y-3\right)\left(x-y+3\right)\)

i) \(7x\left(x-2021\right)-x+2021\)

\(\left(x-2021\right)\left(7x-1\right)\)

j) \(\left(3x+1\right)^2-\left(2x-3\right)^2\)

\(\left(3x+1-2x+3\right)\left(3x+1+2x-3\right)\)

\(\left(x+4\right)\left(5x-2\right)\)

\(x^2-2xy+y^2-9z^2=\left(x-y\right)^2-\left(3z\right)^2=\left(x-y-3z\right)\left(x-y+3z\right)\)

\(x^2+2xy+y^2-9z^2=\left(x^2+2xy+y^2\right)-\left(3z\right)^2\)

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

đề bài là gì?-..-

phân tích các đa thức sau thnahf nhân tử

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

\(\Leftrightarrow\left(x-1\right)^2-4\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1-4\right)\left(x-1\right)=0\Leftrightarrow x=5;1\)