a: =>A-B=3x^2y-4xy^2+x^2y-2xy^2=4x^2y-6xy^2

b: =>B-A=-7xy^2+8x^2y-5xy^2+6x^2y=-12xy^2+14x^2y

=>A-B=12xy^2-14x^2y

c: =>B-A=8x^2y^3-4x^3y-3x^2y^3+5x^3y^2=5x^2y^3+x^3y^2

=>A-B=-5x^2y^3-x^3y^2

d: =>A-B=2x^2y^3-7x^3y+6x^2y^3+3x^3y^2=8x^2y^3-7x^3y+3x^3y^2

a: \(A=31x^2y^3-2xy^3+\dfrac{1}{4}x^2y^2+2\)

\(B=2xy^3+\dfrac{3}{4}x^2y^2-31x^2y^3-x^2-5\)

P=\(A+B=x^2y^2-x^2-3\)

\(A-B=62x^2y^3-4xy^3-\dfrac{1}{2}x^2y^2+x^2+7\)

b: Khi x=6 và y=-1/3 thì \(P=\left(6\cdot\dfrac{-1}{3}\right)^2-6^2-3=4-36-3=1-36=-35\)

Sửa đề: \(D=4x^2+y^2+2xy-8x+2y+5\)

\(=x^2+2xy+y^2+2x+2y+3x^2-10x+5\)

\(=\left(x+y\right)^2+2\left(x+y\right)+1+3x^2-10x+4\)

\(=\left(x+y+1\right)^2+3\left(x^2-\frac{10}{3}x+\frac43\right)\)

\(=\left(x+y+1\right)^2+3\left(x^2-2\cdot x\cdot\frac53+\frac{25}{9}-\frac{13}{9}\right)=\left(x+y+1\right)^2+3\left(x-\frac53\right)^2-\frac{13}{3}\ge-\frac{13}{3}\forall x,y\)

Dấu '=' xảy ra khi \(\begin{cases}x+y+1=0\\ x-\frac53=0\end{cases}\Rightarrow\begin{cases}x=\frac53\\ y=-x-1=-\frac53-1=-\frac83\end{cases}\)

a: \(A=x^2-3x+\dfrac{9}{4}-\dfrac{5}{4}=\left(x-\dfrac{3}{2}\right)^2-\dfrac{5}{4}>=-\dfrac{5}{4}\)

Dấu '=' xảy ra khi x=3/2

c: \(x^2-x+2=\left(x-\dfrac{1}{2}\right)^2+\dfrac{7}{4}>=\dfrac{7}{4}\)

=>\(\dfrac{3}{\left(x-\dfrac{1}{2}\right)^2+\dfrac{7}{4}}< =3:\dfrac{7}{4}=\dfrac{12}{7}\)

=>C>=-12/7

Dấu '=' xảy ra khi x=1/2

mấy bn ơi, giúp mk nhanh vs nha!!!!!!!!!!!

a/ A = 2x² + y² - 2xy - 2x + 3

= (x² - 2xy + y²) + (x² - 2x + 1) + 2

= (x - y)² + (x - 1)² + 2\(\ge2\)

\(2A=\dfrac{2x^2+2y^2}{x^2+2xy+y^2}=1+\dfrac{x^2-2xy+y^2}{\left(x+y\right)^2}=1+\dfrac{\left(x-y\right)^2}{\left(x+y\right)^2}\ge1\text{ nên: }A\ge\dfrac{1}{2}\text{ hay: }A_{min}=\dfrac{1}{2}\text{ Dấu }"="\text{ xảy ra khi: }x=y\text{ khác 0}\)