x,y . xy,x = xy,xy

0,1 * xy,x = 1,01

xy,x= 1,01

x= 1 ; y=0

x,y . x,y =xy,xy

xy : 10 x xyx :10 = xyxy : 100

xy : 10 x xyx = xyxy :100 x 10

xy : 10 x xyx = xyxy :10

xy x xyx = xyxy :10 x 10

xy x xyx = xyxy

xyx = xyxy : xy

xyx = 101

=> x=1, y=0

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X=1

Y=0

\(6xy=x+y\ge2\sqrt[]{xy}\Rightarrow\sqrt{xy}\ge\dfrac{1}{3}\Rightarrow xy\ge\dfrac{1}{9}\Rightarrow\dfrac{1}{xy}\le9\)

\(M=\dfrac{\dfrac{x+1}{xy+1}+\dfrac{xy+x}{1-xy}+1}{1+\dfrac{xy+x}{1-xy}-\dfrac{x+1}{xy+1}}=\dfrac{\dfrac{x+1}{xy+1}+\dfrac{x+1}{1-xy}}{\dfrac{x+1}{1-xy}-\dfrac{x+1}{xy+1}}=\dfrac{\dfrac{1}{1-xy}+\dfrac{1}{1+xy}}{\dfrac{1}{1-xy}-\dfrac{1}{1+xy}}\)

\(M=\dfrac{1+xy+1-xy}{1+xy-1+xy}=\dfrac{2}{2xy}=\dfrac{1}{xy}\le9\)

Dấu "=" xảy ra khi \(x=y=\dfrac{1}{3}\)

x,y X xy,x = xy,xy

(x,y X 10) X ( xy,x X 10 ) = xy,xy X 100

xy              X     xyx           = xyxy

xy              X     xyx            = xy X 100 + xy

xy               X    xyx             = 101 X   xy

xy  X  (xyx - 101 )                = 0

              xyx                         = 101

               xy                           = 10

các chữ số cơ mà

a: =>xy-x+y=0

=>x(y-1)+y-1=-1

=>(y-1)(x+1)=-1

=>(x+1;y-1) thuộc {(1;-1); (-1;1)}

=>(x,y) thuộc {(0;0); (-2;2)}

b: =>x(y+2)+y-1=0

=>x(y+2)+y+2-3=0

=>(y+2)(x+1)=3

=>(x+1;y+2) thuộc {(1;3); (3;1); (-1;-3); (-3;-1)}

=>(x,y) thuộc {(0;1); (2;-1); (-2;-5); (-4;-3)}

c:

y>=3

=>y+5>=8

=>y(x-7)+5x-35=-35

=>(x-7)(y+5)=-35

mà y+5>=8

nên (y+5;x-7) thuộc (35;-1)

=>(y;x) thuộc {(30;6)}