Ta có

\(1+2+3+4+...+x=20100\)

\(\left(x+1\right)\times x\div2=20100\)

\(\left(x+1\right)\times x=20100\times2\)

\(\left(x+1\right)\times x=40200\)

Mà \(40200=201\times200\)

\(\Rightarrow\left(x+1\right)\times x=201\times200\)

\(\Rightarrow x=200\)

Vậy x = 200

ý mày là 1 + 2 + 3 + 4 + 5 + ... + x = 20100 ???

1+2+3+....+x=20100

<=> (x+1)x/2=20100

<=> x(x+1)=40200=200.201

<=> x=200 ( vì x và x+1 là 2 số  tự nhiên liên tiếp)

1 + 2 + 3 + 4 + ... + x = 20100

<=> (x + 1).(x - 1 + 1) : 2 = 20100

<=> (x + 1). x = 20100.2 = 40200

<=> (x + 1). x = 201.200

<=> x = 200

Chúc bạn học tốt !!!

24 ⋮ x và 36 ⋮ x 

\(\Rightarrow x\inƯC\left(24,36\right)\)

Mà: \(ƯC\left(24,36\right)=\left\{1;2;3;4;6;12\right\}\)

\(5\le x\le20\)

\(\Rightarrow x\in\left\{6;12\right\}\)

_______________

100 ⋮ x và 50 ⋮ x

\(\Rightarrow x\inƯC\left(100,50\right)\)

Mà: \(ƯC\left(100;50\right)=\left\{1;2;5;10;25;50\right\}\)

\(3\le x\le15\)

\(\Rightarrow x\in\left\{5;10\right\}\)

24 ⋮ x và 36 ⋮ x 

$\Rightarrow x\in ƯC\left(24,36\right)$

Mà: $ƯC\left(24,36\right)=\left\{1;2;3;4;6;12\right\}$

$5\le x\le 20$

$\Rightarrow x\in \left\{6;12\right\}$

_______________

100 ⋮ x và 50 ⋮ x

$\Rightarrow x\in ƯC\left(100,50\right)$

Mà: $ƯC\left(100;50\right)=\left\{1;2;5;10;25;50\right\}$

$3\le x\le 15$

$\Rightarrow x\in \left\{5;10\right\}$

a) [ 316 – ( 25 . 4 + 16 )] : 8 – 24

=( 316 – 116 ) : 8 – 24 = 200 ∶ 8 – 24 = 25 – 24 = 1

b) | -15| + (-27) + 8 + | - 23|

= 15 – 27 + 8 + 23 = 19

c)  5 8   :   5 6   +   2 2   .   3 3   -   2010 0  =  5 2 + 4 . 27 – 1 = 25 + 108 – 1 = 132

Lời giải:
$y: \frac{1}{8}+y\times 92=20100$

$y\times 8+y\times 92=20100$

$y\times (8+92)=20100$

$y\times 100=20100$

$y=20100:100=201$

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$y: \frac{1}{25}+y\times 75=25000$

$y\times 25+y\times 75=25000$

$y\times (25+75)=25000$

$y\times 100=25000$

$y=25000:100=250$

c)  5 8 : 5 6 + 2 2 . 3 3 - 2010 0  = 52 + 4 . 27 – 1 = 25 + 108 – 1 = 132