y / 2x2-xy+4x / 2xy-x2
1 / (x-y)(y-z) + 1 / (y-z)(z-x) + 1 / (z-x)(x-y)
x-y / xy + y-z / yz + z-x / zx
Thực hiện pt
Những câu hỏi liên quan
(\sqrt((x+yz)(y+xz)))/(xy+z)+(\sqrt((y+xz)(z+xy)))/(x+yz)+(\sqrt((x+yz)(z+xy)))/(y+xz)
Với x,y,z>0 thỏa mãn x+y+z=1
chứng minh rằng: (x-y)/(1+xy) + (y-z)/(1+yz) +(z-x)/(1+zx) = (x-y)(y-z)(z-x)/(1+xy)(1+yz)(1+zx)
Ta có:
\(\dfrac{x-y}{1+xy}\)+\(\dfrac{y-z}{1+yz}\)+\(\dfrac{z-x}{1+xz}\) = \(\dfrac{x-y}{1+xy}\)+\(\dfrac{-\left(x-y\right)-\left(z-x\right)}{1+yz}\)+\(\dfrac{z-x}{1+xz}\)
=\(\dfrac{x-y}{1+xy}\)\(-\dfrac{x-y}{1+yz}\) \(-\dfrac{z-x}{1+yz}\)+\(\dfrac{z-x}{1+xz}\)
= \(\left(x-y\right)\)\(\left(\dfrac{\left(1+yz\right)-\left(1+xy\right)}{\left(1+yz\right)\left(1+xy\right)}\right)\)+(\(z-x\))\(\left(\dfrac{\left(1+yz\right)-\left(1+zx\right)}{\left(1+yz\right)\left(1+zx\right)}\right)\)
=\(\left(x-y\right)\)\(\dfrac{y\left(z-x\right)}{\left(1+yz\right)\left(1+xy\right)}\)+(\(z-x\))\(\dfrac{-z\left(x-y\right)}{\left(1+yz\right)\left(1+zx\right)}\)
=\(\left(\dfrac{\left(x-y\right)\left(z-x\right)}{1+yz}\right)\)\(\left(\dfrac{y\left(1+xz\right)-z\left(1+xy\right)}{\left(1+xz\right)\left(1+xy\right)}\right)\)
=đpcm
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Thực hiện phép tính:(1)/((y-z)(x^2+xz-y^2-yz))+(1)/((z-x)(y^2+zy-z^2-xz))+(1)/((x-y)(x^2+yz-z^2-xy|)
Phân tích các đa thức sau thành nhân tử
a,2x2+3xy-14y2
b,(x-7)(x-5)(x-3)(x-1)+7
c,(x-3)2+(x-3)(3x-1)-2(3x-1)2
d,xy(x-y)+yz(y-z)+zx(z-x)
f,x(y+z)2+y(z+x)2+z(x+y)2-4xyz
a: \(2x^2+3xy-14y^2\)
\(=2x^2+7xy-4xy-14y^2\)
\(=\left(2x^2+7xy\right)-\left(4xy+14y^2\right)\)
\(=x\left(2x+7y\right)-2y\left(2x+7y\right)\)
\(=\left(2x+7y\right)\left(x-2y\right)\)
b: \(\left(x-7\right)\left(x-5\right)\left(x-3\right)\left(x-1\right)+7\)
\(=\left(x-7\right)\left(x-1\right)\left(x-5\right)\left(x-3\right)+7\)
\(=\left(x^2-8x+7\right)\left(x^2-8x+15\right)+7\)
\(=\left(x^2-8x\right)^2+15\left(x^2-8x\right)+7\left(x^2-8x\right)+105+7\)
\(=\left(x^2-8x\right)^2+22\left(x^2-8x\right)+112\)
\(=\left(x^2-8x\right)^2+8\left(x^2-8x\right)+14\left(x^2-8x\right)+112\)
\(=\left(x^2-8x\right)\left(x^2-8x+8\right)+14\left(x^2-8x+8\right)\)
\(=\left(x^2-8x+8\right)\left(x^2-8x+14\right)\)
c: \(\left(x-3\right)^2+\left(x-3\right)\left(3x-1\right)-2\left(3x-1\right)^2\)
\(=\left(x-3\right)^2+2\left(x-3\right)\left(3x-1\right)-\left(x-3\right)\left(3x-1\right)-2\left(3x-1\right)^2\)
\(=\left(x-3\right)\left[\left(x-3\right)+2\left(3x-1\right)\right]-\left(3x-1\right)\left[\left(x-3\right)+2\left(3x-1\right)\right]\)
\(=\left(x-3+6x-2\right)\left(x-3-3x+1\right)\)
\(=\left(7x-5\right)\left(-2x-2\right)\)
\(=-2\left(x+1\right)\left(7x-5\right)\)
d: \(xy\left(x-y\right)+yz\left(y-z\right)+zx\left(z-x\right)\)
\(=x^2y-xy^2+y^2z-yz^2+zx\left(z-x\right)\)
\(=\left(x^2y-yz^2\right)-\left(xy^2-y^2z\right)+xz\left(z-x\right)\)
\(=y\left(x^2-z^2\right)-y^2\left(x-z\right)-xz\left(x-z\right)\)
\(=y\cdot\left(x-z\right)\left(x+z\right)-\left(x-z\right)\left(y^2+xz\right)\)
\(=\left(x-z\right)\left(xy+zy-y^2-xz\right)\)
\(=\left(x-z\right)\left[\left(xy-y^2\right)+\left(zy-zx\right)\right]\)
\(=\left(x-z\right)\left[y\cdot\left(x-y\right)-z\left(x-y\right)\right]\)
\(=\left(x-z\right)\left(x-y\right)\left(y-z\right)\)
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x ≠ y ≠ z thoả mãn 1/z+1/y+1/z=0.Tính M= yz/(x^2+2yz)+xz/(y^2+2xz)+xy/(z^2+2xy)
1.Giải hệ pt1)hept{begin{cases}frac{1}{x}+frac{1}{y}+frac{1}{z}3xy+yz+zx3frac{1}{1+x+xy}+frac{1}{1+y+yz}+frac{1}{1+z+zx}xend{cases}}2)hept{begin{cases}xy+yz+zx3left(x+yright)left(y+zright)sqrt{3}zleft(1+y^2right)left(y+zright)left(z+xright)sqrt{3}xleft(1+z^2right)end{cases}}3)hept{begin{cases}xy+yz+zx31+x^2left(y+zright)+xyz4y1+y^2left(z+xright)+xyz4zend{cases}}
Đọc tiếp
1.Giải hệ pt
1)\(\hept{\begin{cases}\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=3\\xy+yz+zx=3\\\frac{1}{1+x+xy}+\frac{1}{1+y+yz}+\frac{1}{1+z+zx}=x\end{cases}}\)
2)\(\hept{\begin{cases}xy+yz+zx=3\\\left(x+y\right)\left(y+z\right)=\sqrt{3}z\left(1+y^2\right)\\\left(y+z\right)\left(z+x\right)=\sqrt{3}x\left(1+z^2\right)\end{cases}}\)
3)\(\hept{\begin{cases}xy+yz+zx=3\\1+x^2\left(y+z\right)+xyz=4y\\1+y^2\left(z+x\right)+xyz=4z\end{cases}}\)
A=x^2+xy-5x-5y với x=15x1/5;y=14x4/5
B=xyz-xy-yz-zx+x+y+z-1 với x=9;y=51;z=101
C=y^3+4x^2y+4xy+8x^3+2xy^2 với 2x+y=1
cho x,y,z thỏa mãn x^2=yz,y^2=xy,z^2xy cmr x=y=z
Ta có : y2 = xy \(\Rightarrow\)x = y ( 1 )
x2 = yz hay x2 = xz \(\Rightarrow\)x = z ( 2 )
Từ ( 1 ) và ( 2 ) \(\Rightarrow\)x = y = z
Vậy x = y = z
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11. xyz - xy - yz - zx + x + y + z - 1
12. xy(x + y) + yz(y + z) + zx(z + x) + 2xyz
13. xy(x + y) + yz(y + z) + zx(z + x) + 3xyz
giúp mik vs mik đang cần gấp =(((
13:
xy(x+y)+yz(y+z)+xz(x+z)+2xyz
= xy(x + y) + yz(y + z) + xyz + xz(x + z) + xyz
= xy(x + y) + yz(y + z + x) + xz(x + z + y)
= xy(x + y) + z(x + y + z)(y + x)
= (x + y)(xy + zx + zy + z²)
= (x + y)[x(y + z) + z(y + z)]
= (x + y)(y + z)(z + x)
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