Question

(x-1)+(x-2)+...+(x-10)=165

Answer 1

Coi x - 10 là y.

=> x - 9 là y + 1

........... x - 1 là y + 9.

Ta có : (x-1)+(x-2)+...+(x-10) = 165

<=> (y+9)+(y+8)+...+y = 165.

=> 10y + 45 = 165.

=> 10y = 120.

=> y = 12.

Tương đương : x - 1 = 12 + 9

=> x = 21 + 1 = 22.

Vậy x là 22.

Answer 2

Coi \(x-10=y\)

\(\Rightarrow x-9=y+1\)

\(\left(x-1\right)+\left(x-2\right)+...+\left(x-10\right)=165\)

Ta có hai số hạng liền trước số 10

10 - 1 = 9 ; 9 - 1 = 8

\(\Leftrightarrow\left(y+9\right)+\left(y+8\right)+...+y=165\)

\(=10y+45=165\)

\(\Rightarrow10y=165-45=120\)

\(\Rightarrow y=120:10=12\)

Ta có x - 1

\(\Rightarrow x=21+1=22\)

Answer 3

\(\left(x-1\right)+\left(x-2\right)+...+\left(x-10\right)=165\)

\(\Leftrightarrow\left(x+x+...+x\right)-\left(1+2+...+10\right)=165\)

\(\Leftrightarrow10x-55=165\)

\(\Leftrightarrow10x=220\Rightarrow x=22\)

Answer 4

Ta có :

\(\left(x-1\right)+\left(x-2\right)+..........+\left(x-10\right)=165\)

\(\Leftrightarrow\left(x+x+.....+x\right)-\left(1+2+....+10\right)=165\)

\(\Leftrightarrow10x-55=165\)

\(\Leftrightarrow10x=110\)

\(\Leftrightarrow x=10\)

Vậy ..................

Answer 5

nhục qá, bài này còn sai! :((

Answer 6

C1: \(\left(x-1\right)+\left(x-20\right)+...+\left(x-10\right)=165\)

\(\left(x+x+...+x\right)-\left(1+2+...+10\right)=165\)

\(\left(x.10\right)+\left(1+10\right).10:2=165\)

\(\left(x.10\right)+55=165\)

\(x.10=165-55\)

\(x.10=110\)

\(x=110:10\)

\(x=11\)

Vậy \(x=11\)

C2: \(\left(x-1\right)+\left(x-20\right)+...+\left(x-10\right)=165\)

\(\Rightarrow\) \(10x-\left(1+2+...+10\right)=165\)

\(\Rightarrow\) \(10x+55=165\)

\(\Rightarrow\) \(10x=165-55\)

\(\Rightarrow\) \(10x=165-55\)

\(\Rightarrow\) \(10x=110\)

\(\Rightarrow\) \(x=110:10\)

\(\Rightarrow\) \(x=11\)

Vậy \(x=11\)