x + y = x.y

=> xy - x - y = 0

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

=> x(y - 1) - (y - 1) = 1

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

=> x - 1 = y - 1 = 1 hoặc x - 1 = y - 1 = -1

=> x = y = 2 hoặc x = y = 0

\(-\left(-a+b+c\right)+\left(b-c-1\right)=\left(b-c+6\right)-\left(7-a+b\right)+c\)

\(a-b-c+b-c-1=b-c+6-7+a-b+c\)

\(a-2c-1=a-1\)

\(-2c\ne0\)hay đẳng thức ko xảy ra 

a, (x+1) + (x+3) + ...... + (x+99) = 100

(x+x+x+...+x) + (1+3+....+99) = 100

(x.50) + 2450 = 100

x.50 = 100 - 2450

x.50 = -2350

x = -2350 : 50

x = -47

b, (x-3) + (x-2) + (x-1) + ........ + 10 + 11 = 11

(x+x+x) - (3+2+1) + (1+2+3+...+10+11) = 11

3x - 6 + 66 = 11

3x + 60 = 11

3x = 11 - 60

3x = 49

x = \(\frac{49}{3}\)

phần b mk ko chắc lắm

chỗ trong ... là gì thế ?

a: \(\Leftrightarrow x-3\inƯ\left(21\right)\)

\(\Leftrightarrow x-3\in\left\{-3;-1;1;3;7;21\right\}\)

hay \(x\in\left\{0;2;4;6;10;24\right\}\)

b: \(\Leftrightarrow x-1\in\left\{1;-1;17\right\}\)

hay \(x\in\left\{2;0;18\right\}\)

c: \(\Leftrightarrow2x-1+4⋮2x-1\)

\(\Leftrightarrow2x-1\in\left\{1;-1\right\}\)

hay \(x\in\left\{1;0\right\}\)

d: \(\Leftrightarrow x^2+x+3⋮x+1\)

\(\Leftrightarrow x+1\inƯ\left(3\right)\)

\(\Leftrightarrow x+1\in\left\{1;3\right\}\)

hay \(x\in\left\{0;2\right\}\)

a) (x+1)+(x+3)+(x+5)+...+(x+99)=0  

=> 99x + (1 + 3 + 5 +...+ 99) = 0

Áp dụng công thức tính dãy số ta có :

1 + 3 + 5 + ... + 99 = \(\frac{\left[\left(99-1\right):2+1\right].\left(99+1\right)}{2}=\frac{50.100}{2}=50.50=2500\)

=> 99x + 2500 = 0

=> 99x = -2500

=> x = \(\frac{-2500}{99}=25,\left(25\right)\)

(x+1)+(x+3)+(x+5)+. . .+(x+99)=0

(x+x+. . .+x)+(1+3+5+. . .+99)=0

         50x+2500=0

           50x=-2500

               x=-50

\(\left(x+1\right)+\left(x+3\right)+.....+\left(x+99\right)=0\)

\(\left(x+x+......+x\right)+\left(1+3+........+99\right)=0\)

\(50x+2500=0\)

\(50x=-2500\)

\(x=-50\)

1^2 + 2^2 + 3^2 + ... + 99^2

= 1(2 - 1) + 2(3 - 1) + 3(4- 1) + ... + 98(99-1) + 99(100 -1)

= 1.2 -1.1 + 2.3 - 2.1 + 3.4 - 3.1 + ... + 98.99 + 98.1 + 99.100 - 99

= (1.2 + 2.3 + 3.4 + ... + 99.100) - (1 + 2 + 3 + ... + 99)

đặt S = 1.2 + 2.3 + 3.4 + ... + 99.100

3S = 1.2.3 + 2.3.3 + 3.4.3 + ... + 99.100.3

3S = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + .... + 99.100.(101 - 98)

3S = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 99.100.101 - 98.99.100

3S = 99.100.101

S = 99.100.101 : 3 = 333300

A = 1 + 2 + 3 + ... + 99

A = (99 + 1).99 : 2 = 4950

Tinh ra là :

333300 - 4950 = 328350