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

\(=2\left(x-y\right)-xy\left(x-y\right)\)

\(=\left(x-y\right)\left(2-xy\right)\)

\(=\left(-\dfrac{1}{2}-\dfrac{-1}{3}\right)\left(2-\dfrac{-1}{2}\cdot\dfrac{-1}{3}\right)\)

\(=\left(\dfrac{1}{3}-\dfrac{1}{2}\right)\cdot\left(2-\dfrac{1}{6}\right)\)

\(=\dfrac{-1}{6}\cdot\dfrac{11}{6}=-\dfrac{11}{36}\)

a: A=x^2y(2/3+3+1)=14/3*x^2y

=14/3*3^2*(-1/7)

=-2*3=-6

Bài 3: 

a: Ta có: C=A+B

\(=x^2-2y+xy+1+x^2+y-x^2y^2-1\)

\(=2x^2-y+xy-x^2y^2\)

b: Ta có: C+A=B

\(\Leftrightarrow C=B-A\)

\(=x^2+y-x^2y^2-1-x^2+2y-xy-1\)

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

a: \(\dfrac{1}{2}x^2y\left(2x^3-\dfrac{2}{5}xy^2-1\right)\)

\(=x^5y-\dfrac{1}{5}x^3y^3-x^2y\)

b: \(\left(\dfrac{1}{2}x-5\right)\left(x^2-2x+3\right)\)

\(=\dfrac{1}{2}x^3-x^2+\dfrac{3}{2}x-5x^2+10x-15\)

\(=\dfrac{1}{3}x^3-6x^2+\dfrac{23}{2}x-15\)

6 tháng 5 2023

`a)` Thay `x=2` vào `B` có: `B=[-10]/[2-4]=5`

`b)` Với `x ne -1;x ne -5` có:

`A=[(x+2)(x+1)-5x-1-(x+5)]/[(x+1)(x+5)]`

`A=[x^2+x+2x+2-5x-1-x-5]/[(x+1)(x+5)]`

`A=[x^2-3x-4]/[(x+1)(x+5)]`

`A=[(x+1)(x-4)]/[(x+1)(x+5)]`

`A=[x-4]/[x+5]`

`c)` Với `x ne -5; x ne -1; x ne 4` có:

`P=A.B=[x-4]/[x+5].[-10]/[x-4]`

           `=[-10]/[x+5]`

Để `P` nguyên `<=>[-10]/[x+5] in ZZ`

    `=>x+5 in Ư_{-10}`

Mà `Ư_{-10}={+-1;+-2;+-5;+-10}`

`=>x={-4;-6;-3;-7;0;-10;5;-15}` (t/m đk)

9 tháng 6 2021

\(a^2-2a+6b+b^2=-10\\ \Leftrightarrow a^2-2a+1+b^2+6b+9=0\\ \Leftrightarrow\left(a-1\right)^2+\left(b+3\right)^2=0\\ \Leftrightarrow\left\{{}\begin{matrix}a=1\\b=-3\end{matrix}\right.\)

Vậy \(\left(a;b\right)=\left(1;-3\right)\)

9 tháng 6 2021

\(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=0\\ \Leftrightarrow xy+yz+zx=0\\ \Rightarrow\left\{{}\begin{matrix}xy+yz=-zx\\xy+zx=-yz\\yz+zx=-xy\end{matrix}\right.\)

Ta có: 

\(A=\dfrac{xz+yz}{z^2}+\dfrac{xy+yz}{y^2}+\dfrac{xy+xz}{x^2}\\ =\dfrac{-xy}{z^2}+\dfrac{-xz}{y^2}+\dfrac{-yz}{x^2}\\ =-xyz\cdot\left(\dfrac{1}{x^3}+\dfrac{1}{y^3}+\dfrac{1}{z^3}\right)\\ =-xyz\cdot\left(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}\right)\left(\dfrac{1}{x^2}+\dfrac{1}{y^2}+\dfrac{1}{z^2}-\dfrac{2}{xy}-\dfrac{2}{yz}-\dfrac{2}{xz}\right)\\ =0\)

a: \(A=\dfrac{x^2+4x+4+4x^2-x^2+4x-4}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x-2}{x\left(x^2+x+2\right)}\)

\(=\dfrac{4x^2+8x}{\left(x+2\right)}\cdot\dfrac{1}{x\left(x^2+x+2\right)}=\dfrac{4}{x^2+x+2}\)

|x+3|=5

=>x=2(loại) hoặc x=-8(nhận)

Khi x=-8 thì \(A=\dfrac{4}{64-8+2}=\dfrac{4}{58}=\dfrac{2}{29}\)

b: A nguyên

=>x^2+x+2 thuộc {1;-1;2;-2;4;-4}

=>x^2+x+2=2 hoặc x^2+x+2=4

=>x^2+x-2=0 hoặc x(x+1)=0

=>\(x\in\left\{1;0;-1\right\}\)

22 tháng 7 2023

a) \(\dfrac{x^2-2x+1}{x+2}=\dfrac{\left(x-1\right)^2}{x+2}\)

Khi x=-3 ta có:

\(\dfrac{\left(-3-1\right)^2}{-3+2}=\dfrac{\left(-4\right)^2}{-1}=-4\)

Khi x=1 ta có:
\(\dfrac{\left(1-1\right)^2}{1+2}=0\)

b) \(\dfrac{xy+3y^2}{x+y}=\dfrac{y\left(x+3y\right)}{x+y}\)

Khi x=3 y=-1 ta có:

\(\dfrac{-1\cdot\left(3+3\cdot-1\right)}{3\cdot-1}=0\)