x*(y+2)-2y=-1
Giải hệ pt:
a)(x+√(x^2+4))(y+√(y^2+1))=2 và 27x^6=x^3-8y+2
b)(8x-3)√(2x-1) -y-4y^3=0 và 4x^2-8x+2y^3+y^2-2y+3=0
c) x(1+y-x)=-2y^2-y và x(√2y -2)=y(√(x-1)-2)
d) √(x+2y)+√(2x-y)+x^2y=√x+√3y+xy^2 và 2(1-y)√(x^2+2y-1)=y^2-2x-1
e)(y-2x+√y-√x)/√xy +1=0 và √(1-xy) +x^2-y^2=0
CÁC BẠN ƠI..GIÚP MK VS Ạ...MAI MK HOK R...CẢM ƠM TRƯỚC Ạ...☺️☺️☺️
Rút gọn biểu thức:
A= (x^2-y)(y+1)+x^2y^2-1/(x^2+y)(y+1)+x^2y^2+1
B= x^2(y-z)+y^2(z-x)+z^2(x-y)/x^2y-x^2z+y^2z-y^3
đã tắt máy chưa để cho mình giải nha
M)(x^2-2xy+y^2)(x-y) N)-(x-y)(x^2+xy-1) Ờ)-(x^2-2y)(x+y^2-1) P)(1/2x-1)(2x-3) Q)(x-1/2y)(x-1/2y) R)(x^2-2x+3)(1/2x-5)
m: (x-y)(x^2-2xy+y^2)
=(x-y)*(x-y)^2
=(x-y)^3
=x^3-3x^2y+3xy^2-y^3
n: =-(x^3+x^2y-x-x^2y-xy^2+y)
=-x^3+x+xy^2-y
o: =-(x^3+x^2y^2-x^2-2xy-2y^3+2y)
=-x^3-x^2y^2+x^2+2xy+2y^3-2y
p: (1/2x-1)(2x-3)
=1/2x*2x-1/2x*3-2x+3
=x^2-3/2x-2x+3
=x^2-7/2x+3
q: (x-1/2y)(x-1/2y)
=(x-1/2y)^2
=x^2-xy+1/4y^2
r: (x^2-2x+3)(1/2x-5)
=1/2x^3-5x^2-x^2+10x+3/2x-15
=1/2x^3-6x^2+11,5x-15
1) \(\left\{{}\begin{matrix}xy+x+y=x^2-2y^2\\x\sqrt{2y}-y\sqrt{x-1}=2x-2y\end{matrix}\right.\)
2) \(\left\{{}\begin{matrix}2x^2+y^2-3xy+3x-2y+1=0\\4x^2-y^2+x+4=\sqrt{2x+y}+\sqrt{x+4y}\end{matrix}\right.\)
g)(x+3y)(x-3y+2) h)(x+2y((x-2y+3) I)(x^2-xy+y^2)(x+y) J)(x^2-xy+y^2)(x+y) K)(5x-2y)(x^2-xy-1) L)(x^2y^2-xy+y)(x-y)
g: (x+3y)(x-3y+2)
=(x+3y)(x-3y)+2(x+3y)
=x^2-9y^2+2x+6y
h: (x+2y)(x-2y+3)
=(x+2y)(x-2y)+3(x+2y)
=x^2-4y^2+3x+6y
i: (x^2-xy+y^2)(x+y)
=x^3+x^2y-x^2y-xy^2+xy^2+y^3
=x^3+y^3
j: (x+y)(x^2-xy+y^2)=x^3+y^3
k: (5x-2y)(x^2-xy-1)
=5x*x^2-5x*xy-5x-2y*x^2+2y*xy+2y
=5x^3-5x^2y-5x-2x^2y+2xy^2+2y
=5x^3-7x^2y+2xy^2-5x+2y
l: (x^2y^2-xy+y)(x-y)
=x^3y^2-x^2y^3-x^2y^2+xy^2+xy-y^2
cho 2 số thực `x,y` thỏa mãn `x>0,y>2,x`\(\ne\)`2y`. CMR: \(\left(\dfrac{x-y}{2y-x}-\dfrac{x^2+y^2+y-2}{x^2-xy-2y^2}\right)\left(2x^2+y+2\right):\dfrac{x^4+4x^2y^2+y^4-4}{x^2+y+xy+x}=\dfrac{x+1}{2y-x}\)
Đề bài sai, đề đúng thì phân thức đằng sau dấu chia phải là:
\(\dfrac{4x^4+4x^2y+y^2-4}{x^2+y+xy+x}\)
\(\left\{{}\begin{matrix}\left(1-y\right)\sqrt{x^2+2y^2}=x+2y+3xy\\\sqrt{y+1}+\sqrt{x^2+2y^2}=2y-x\end{matrix}\right.\)
chứng minh đẳng thức
\(\left(\frac{x-y}{2y-x}-\frac{x^2+y^2+y-2}{x^2-xy-2y^2}\right):\frac{x^4+4x^2y^2+y^4-4}{x^2+y+xy+x}:\frac{1}{2x^2+y+2}=\frac{x+1}{2y-x}\)
Rút gọn biểu thức:
A= (x^2-y)(y+1)+x^2y^2-1
(x^2+y)(Y+1)+x^2y^2+1
B =x^2(y-z)+y^2(z-x)+z^2(x-y)
x^2y-x^2z+y^2z-y^3
\(B=\frac{x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)}{x^2y-x^2z+y^2z-y^3}\)
\(=\frac{x^2y-x^2z+zy^2-xy^2+z^2x-z^2y}{x^2\left(y-z\right)-y^2\left(y-z\right)}\)
\(=\frac{\left(x^2y-z^2y\right)-\left(xy^2-zy^2\right)-\left(x^2z-z^2x\right)}{\left(x^2-y^2\right)\left(y-z\right)}\)
\(=\frac{\left[y\left(x+z\right)-y^2-xz\right]\left(x-z\right)}{\left(x-y\right)\left(x+y\right)\left(y-z\right)}\)
\(=\frac{\left(xy+zy-y^2-xz\right)\left(x-z\right)}{\left(x-y\right)\left(x+y\right)\left(y-z\right)}\)
\(=\frac{\left[\left(xy-y^2\right)-\left(xz-zy\right)\right]\left(x-z\right)}{\left(x-y\right)\left(x+y\right)\left(y-z\right)}\)
\(=\frac{\left[y\left(x-y\right)-z\left(x-y\right)\right]\left(x-z\right)}{\left(x-y\right)\left(x+y\right)\left(y-z\right)}\)
\(=\frac{\left(y-z\right)\left(x-y\right)\left(x-z\right)}{\left(x-y\right)\left(x+y\right)\left(y-z\right)}\)
\(=\frac{x-z}{x+y}\)
\(A=\frac{\left(x^2-y\right)\left(y+1\right)+x^2y^2-1}{\left(x^2+y\right)\left(y+1\right)+x^2y^2+1}\)
\(=\frac{x^2y-y^2+x^2-y+x^2y^2-1}{x^2y+y^2+x^2+y+x^2y^2+1}\)
\(=\frac{\left(x^2y+x^2\right)+\left(x^2y^2-y^2\right)-\left(y+1\right)}{\left(x^2y+x^2\right)+\left(x^2y^2+y^2\right)+\left(y+1\right)}\)
\(=\frac{x^2\left(y+1\right)+y^2\left(x^2-1\right)-\left(y+1\right)}{x^2\left(y+1\right)+y^2\left(x^2+1\right)+\left(y+1\right)}\)
\(=\frac{\left(x^2-1\right)\left(y+1\right)+y^2\left(x^2-1\right)}{\left(x^2+1\right)\left(y+1\right)+y^2\left(x^2+1\right)}\)
\(=\frac{\left(x^2-1\right)\left(y^2+y+1\right)}{\left(x^2+1\right)\left(y^2+y+1\right)}\)
\(=\frac{x^2-1}{x^2+1}\)
1/Ghpt\(\left\{{}\begin{matrix}x^2+y^2+x^2y^2=1+2xy\\\left(x-y\right)\left(1+xy\right)=1-xy\end{matrix}\right.\)
2/Ghpt\(\left\{{}\begin{matrix}x^2y+y+xy^2+x=18xy\\x^4y^2+y^2+x^2y^4+x^2=208x^2y^2\end{matrix}\right.\)
3/Ghpt\(\left\{{}\begin{matrix}\sqrt{x+3}+\sqrt{y+3}=4\\\dfrac{1}{x}+\dfrac{1}{y}=2\end{matrix}\right.\)
4/ Cho x,y là nghiệm của hệ phương trình
\(\left\{{}\begin{matrix}x+y=m\\x^2+y^2=2m\end{matrix}\right.\)
Tìm min và max của A=xy
5/cho x,y,z thỏa mãn đk
\(\left\{{}\begin{matrix}xy+yz+xz=1\\x^2+y^2+z^2=2\end{matrix}\right.\)
Chứng minh rằng: \(\dfrac{-4}{3}\le x,y,z\le\dfrac{4}{3}\)
6/Ghpt bằng 3 cách\(\left\{{}\begin{matrix}x+y+z=1\\\\x^2+y^2+z^2=1\\x^3+y^3+z^3=1\end{matrix}\right.\)
7/Ghpt\(\left\{{}\begin{matrix}x^3+1=2y\\y^3+1=2x\end{matrix}\right.\)
8/Ghpt\(\left\{{}\begin{matrix}x^2-3y=-2\\y^2-3x=-2\end{matrix}\right.\)
9/Ghpt bằng 2 cách\(\left\{{}\begin{matrix}x+\sqrt{y+3}=3\\y+\sqrt{x+3}=3\end{matrix}\right.\)
10/Ghpt\(\left\{{}\begin{matrix}x+\dfrac{2}{y}=\dfrac{3}{x}\\y+\dfrac{2}{x}=\dfrac{3}{y}\end{matrix}\right.\)
11/Ghpt\(\left\{{}\begin{matrix}\sqrt[3]{3x+5}=y+1\\\sqrt[3]{3y+5}=x+1\end{matrix}\right.\)
12/Ghpt\(\left\{{}\begin{matrix}3x^2y-y^2-2=0\\3y^2x-x^2-2=0\end{matrix}\right.\)
13/Giải các phương trình sau bằng cách đứa về hệ pt đối xứng loại II:
a)\(\left(x^2-3\right)^2-x-3=0\)
b)\(x^2-2=\sqrt{x+2}\)
14/Ghpt:\(\left\{{}\begin{matrix}x^2+y^2+xy=3\\x^2-y^2+xy=1\end{matrix}\right.\)