Tìm x,y thuoc Z
a) x + xy + y=4
b) xy=x+y
c) xy+5x-2y=19
d) x+xy+y=6
e) 197xy-x-y=0
Cho x>y>2
a.chứng minh x+y>4, xy>4
b. x2 -xy>0, y2 -2y>0, xy-y2>0
a: x>2
y>2
=>x+y>2+2=4
x>y>2
=>xy>2^2=4
b: x^2-xy=x(x-y)
x-y>0; x>0
=>x(x-y)>0
=>x^2-xy>0
y>2
=>y-2>0
=>y(y-2)>0
=>y^2-2y>0
x>y và y>2
=>y>0 và x-y>0
=>y(x-y)>0
=>xy-y^2>0
Tìm x,y thuộc Z
a)49-y^2=6(x-2021)^2
b)x^2 + xy + y^2=2x+y
c)x^2 + xy + y^2=x+y
d)x^2 + 3xy + 3y^2 =3y
e)x^2 - 2xy - 5y^2=y+1
Tìm x,y thuộc Z
a)49-y^2=6(x-2021)^2
b)x^2 + xy + y^2=2x+y
c)x^2 + xy + y^2=x+y
d)x^2 + 3xy + 3y^2 =3y
e)x^2 - 2xy - 5y^2=y+1
Tìm x,y thuộc Z
a)49-y^2=6(x-2021)^2
b)x^2 + xy + y^2=2x+y
c)x^2 + xy + y^2=x+y
d)x^2 + 3xy + 3y^2 =3y
e)x^2 - 2xy - 5y^2=y+1
Tìm x,y thuộc Z
a)49-y^2=6(x-2021)^2
b)x^2 + xy + y^2=2x+y
c)x^2 + xy + y^2=x+y
d)x^2 + 3xy + 3y^2 =3y
e)x^2 - 2xy - 5y^2=y+1
Tìm x,y thuộc Z
a)49-y^2=6(x-2021)^2
b)x^2 + xy + y^2=2x+y
c)x^2 + xy + y^2=x+y
d)x^2 + 3xy + 3y^2 =3y
e)x^2 - 2xy - 5y^2=y+1
Tìm x,y thuộc Z
a)49-y^2=6(x-2021)^2
b)x^2 + xy + y^2=2x+y
c)x^2 + xy + y^2=x+y
d)x^2 + 3xy + 3y^2 =3y
e)x^2 - 2xy - 5y^2=y+1
tìm x y thuộc z
a) x+y=xy
b) 2x-xy-2y=3
c) 4x-xy+5y=17
d) 2xy+2n-y=5
a: =>x-xy+y=0
=>x(1-y)+1-y-1=0
=>(x+1)(1-y)=1
=>(x+1)(y-1)=-1
=>\(\left(x+1;y-1\right)\in\left\{\left(-1;1\right);\left(1;-1\right)\right\}\)
=>\(\left(x,y\right)\in\left\{\left(-2;2\right);\left(0;0\right)\right\}\)
b: 2x-xy-2y=3
=>x(2-y)-2y+4=7
=>x(2-y)+2(2-y)=7
=>(x+2)(y-2)=-7
=>\(\left(x+2;y-2\right)\in\left\{\left(1;-7\right);\left(-7;1\right);\left(-1;7\right);\left(7;-1\right)\right\}\)
=>\(\left(x;y\right)\in\left\{\left(-1;-5\right);\left(-9;3\right);\left(-3;9\right);\left(5;1\right)\right\}\)
c: =>x(4-y)+5y-20=-3
=>x(4-y)-5(4-y)=-3
=>(4-y)(x-5)=-3
=>(x-5)(y-4)=3
=>\(\left(x-5;y-4\right)\in\left\{\left(1;3\right);\left(3;1\right);\left(-1;-3\right);\left(-3;-1\right)\right\}\)
=>\(\left(x,y\right)\in\left\{\left(6;9\right);\left(8;5\right);\left(4;1\right);\left(2;3\right)\right\}\)
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