B=3x⁵y+1/3xy⁴+3/4x²y³–1/2x⁵y+2xy–x²y³
Tìm nghiệm nguyên của các phương trình sau:
a) 2xy - 4x - y = 1
b) (2x - 1)(y - 2) = 3
c) 2xy - x - y +1 = 0
d) 2xy - 4x + y = 7
e) 3xy + x - y = 1
f) xy + 3x - 5y = -3
g) 4x + 11y = 4xy
phân tích thành nhân tử
`3x^2 -3xy-5x+5y`
`2x^3 y-2xy^3 -4xy^2 -2xy`
`x^2 -1+2x-y^2`
`x^2 +4x-2xy-4y+4y^2`
`x^3 -2x^2 +x`
`2x^2 +4x+2-2y^2`
a) \(3x^2-3xy-5x+5y\)
\(=\left(3x^2-3xy\right)-\left(5x-5y\right)\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(3x-5\right)\)
b) \(2x^3y-2xy^3-4xy^2-2xy\)
\(=2xy\left(x^2-y^2-2y-1\right)\)
\(=2xy\left[x^2-\left(y^2+2y+1\right)\right]\)
\(=2xy\left[x^2-\left(y+1\right)^2\right]\)
\(=2xy\left(x-y-1\right)\left(x+y+1\right)\)
c) \(x^2+1+2x-y^2\)
\(=\left(x^2+2x+1\right)-y^2\)
\(=\left(x+1\right)^2-y^2\)
\(=\left(x+1+y\right)\left(x+1-y\right)\)
d) \(x^2+4x-2xy-4y+y^2\)
\(=\left(x^2-2xy+y^2\right)+\left(4x-4y\right)\)
\(=\left(x-y\right)^2+4\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y+4\right)\)
e) \(x^3-2x^2+x\)
\(=x\left(x^2-2x+1\right)\)
\(=x\left(x-1\right)^2\)
f) \(2x^2+4x+2-2y^2\)
\(=2\left(x^2+2x+1-y^2\right)\)
\(=2\left[\left(x^2+2x+1\right)+y^2\right]\)
\(=2\left[\left(x+1\right)^2-y^2\right]\)
\(=2\left(x-y+1\right)\left(x+y+1\right)\)
a: =3x(x-y)-5(x-y)
=(x-y)(3x-5)
b: \(=2xy\left(x^2-y^2-2y-1\right)\)
\(=2xy\left[x^2-\left(y^2+2y+1\right)\right]\)
\(=2xy\left(x-y-1\right)\left(x+y+1\right)\)
d:
Sửa đề: x^2+4x-2xy-4y+y^2
=x^2-2xy+y^2+4x-4y
=(x-y)^2+4(x-y)
=(x-y)(x-y+4)
e: =x(x^2-2x+1)
=x(x-1)^2
f: =2(x^2+2x+1-y^2)
=2[(x+1)^2-y^2]
=2(x+1+y)(x+1-y)
CMR a.(x-2)(2x+2x^2)/(x+1)(4x-x^3)=-2/x+2
b. x^2+y^2+2xy-1/x^2-y^2+1+2x=x+y-1x+1-y
c(x^2+2)^2-4x^2/y(x^2+2)-2xy-(x-1)^2-1
d 3y-2--3xy+2x/1-3x-x^3+3x^2=3y-2/(1-x)^2
Tìm nghiệm nguyên của các phương trình sau:
a) 2xy - 4x - y = 1
b) (2x - 1)(y - 2) = 3
c) 2xy - x - y +1 = 0
d) 2xy - 4x + y = 7
e) 3xy + x - y = 1
f) xy + 3x - 5y = -3
g) 4x + 11y = 4xy
Tính giá trị biểu thức;
A=(2x-y)(4x^2-2xy+y^2)+(3x-y)(9x^2+3xy+y^2)-35(x-1)(x^2+x+1)
B=(x+2)^3+(x-2)^3-2x(2x^2+12)
C=(x-1)^3-(x+1)^3+6(x+1)(x-1)
B = (x + 2)3 + (x - 2)3 - 2x(2x2 + 12)
B = (x + 2)(x2 + 2x.2 + 22) + (x - 2)(x2 - 2x.2 + 22) - 2x(2x3 + 12)
B = x3 + 4x3 + 4x + 2x2 + 8x + 8 + x3 - 4x2 + 4x - 2x2 + 8x - 8 - 4x3 - 24x
B = -2x3
Bài 1: Tính:
A=(8x³-4x²):2x²-(4x²-3x):x+2x khi x=-1
Bài 2: Tính:
(3x³-2x²y):x²-(2xy²+x²y):1/3xy
Bài 1: Tìm x, y nguyên biết :
a) 4x + 2xy + y = 7
b) 3x - xy + 2y = 4
c) 2x + 3xy + y = -4
Bài 1: Tìm x, y nguyên biết :
a) 4x + 2xy + y = 7
=> 2.x(y-2)+(y-2)=5
=> ( y-2)(2x+1)= 5
Ta có bảng sau:
2x+1 | -5 | -1 | 1 | 5 |
y-2 | -1 | -5 | 5 | 1 |
x | -3 | -1 | 0 | 2 |
y | 1 | -3 | 7 | 3 |
Điều kiện: t/m
Vậy:....
phần b và c tương tự
b: =>x(3-y)+2y-6=-2
=>-x(y-3)+2(y-3)=-2
=>(y-3)(x-2)=2
=>\(\left(x-2;y-3\right)\in\left\{\left(1;2\right);\left(2;1\right);\left(-1;-2\right);\left(-2;-1\right)\right\}\)
=>\(\left(x,y\right)\in\left\{\left(3;5\right);\left(4;4\right);\left(1;1\right);\left(0;2\right)\right\}\)
c: =>x(3y+2)+y+2/3=-4+2/3=-10/3
=>(y+2/3)(3x+1)=-10/3
=>(3x+1)(3y+2)=-10
=>\(\left(3x+1;3y+2\right)\in\left\{\left(1;-10\right);\left(10;-1\right);\left(-2;5\right);\left(-5;2\right)\right\}\)
=>\(\left(x,y\right)\in\left\{\left(0;-4\right);\left(3;-1\right);\left(-1;1\right);\left(-2;0\right)\right\}\)
Bài 3:
3: \(6x\left(x-y\right)-9y^2+9xy\)
\(=6x\left(x-y\right)+9xy-9y^2\)
\(=6x\left(x-y\right)+9y\left(x-y\right)\)
\(=\left(x-y\right)\left(6x+9y\right)\)
\(=3\left(2x+3y\right)\left(x-y\right)\)
Bài 4:
A = \(\dfrac{5xy^2-3z}{3xy}+\dfrac{4x^2y+3z}{3xy}\)
B = \(\dfrac{3y+5}{y-1}+\dfrac{-y^2-4y}{1-y}+\dfrac{y^2+y+7}{y-1}\)
C = \(\dfrac{6x}{x^2-9}+\dfrac{5x}{x-3}+\dfrac{x}{x+3}\)
D = \(\dfrac{1-3x}{2x}+\dfrac{3x-2}{2x-1}+\dfrac{3x-2}{2x-4x^2}\)
E = \(\dfrac{x^3+2x}{x^3+1}+\dfrac{2x}{x^2-x+1}+\dfrac{1}{x+1}\)
b: \(B=\dfrac{3y+5}{y-1}-\dfrac{-y^2-4y}{y-1}+\dfrac{y^2+y+7}{y-1}\)
\(=\dfrac{3y+5+y^2+4y+y^2+y+7}{y-1}\)
\(=\dfrac{2y^2+8y+12}{y-1}\)