a) x.31+(1+2+3+4+.....+30)=1240

x.31+465=1240

x.31=1240-465

x.31=775

x=775:31

x=25

b) (1+x).x:2=210

(1+x).x=210.2

(1+x).x=420

Vì 1+x và x là 2 số nhiên liên tiếp và 420=20.21

=> x=20

x + ( x + 1 ) + ( x + 2 )+.........+ (x + 30)= 1240

x + ( x . 30 ) + ( 1 + 2 + .... + 30 ) = 1240

x . 31 + ( 1 + 2 + .... + 30 ) = 1240

x.31 +[( 31-1)+1] = 1240

x.31 + [( 30+1)*30:2] = 1240

x.31 + 465 = 1240

x.31 = 1240 - 465

x.31 = 775

x = 775 : 31

x = 25

1+2+3+...+x=210

(x+1).x:2=210

(x+1).x=210.2

(x+1).x=420

(x+1).x=(20+1).20

=>x=20

x+x+x+...+x+(1+2+...+30)=1240

31.x+(1+2+...+30)=1240

31.x+465=1240

31.x=1240-465

31.x=775

x=775:31

x=25

1) x = 25

2) x = 20

a) x+(x+1)+(x+2)+…+(x+30)=1240

=>x+x+1+x+2+x+3+…+x+30=1240

=>x+x+x+…+x+1+2+3+…+30=1240

Từ 1->30 có: (30-1):1+1=30(số)

=>31.x+(30+1).30:2=1240

=>31.x+31.15=1240

=>31.x+465=1240

=>31.x=1240-465

=>31x=775

=>x=775:31

=>x=25

b) 1+2+3+…+x=210

=>x.(x+1):2=210

=>x.(x+1)=420

=>x.(x+1)=20.21=20.(20+1)

=>x=20

Bài 1:

a,x + ( x + 1) + (x + 2) + (x + 3) +....+ (x + 30) = 1240

x + x +x +.... + x + (1 + 2+ 3+ ....+ 30) = 1240

31x + 465 =1240

31x = 1240 - 465

31x = 775

x = 775 : 31

x = 25

b, 1+2+3+...+x=210

\(\frac{x.\left(x+1\right)}{2}=210\)

x(x+1)=210.2

x(x+1)=420

x(x+1)=20.21

=>x=20

BAi 1:

x + (x+1) + (x+2) + (x+3) + ...+ (x+30) = 1240

x + x + x +...+ x + 1 + 2 + 3 + 4 +..........+ 30 =1240

day so 1 + 2 + 3 + ... + 30 co so so hang la:

(30-1):1+1=30

a) 

B(14) = 0; 14; 28; 42; 56; 70; 84; …..

Vì 20 < x < 80 => x ∈ { 28; 42; 56; 70．}

b)

Vì 70 chia hết cho x ѵà 80 chia hết cho x => x ∈ ƯC(70; 80)

Phân tích:

70 = 2 ．5 ．7

80 = 24 ．5

ƯCLN (70; 80) = 2.5=10

ƯC ( 70; 80) = Ư(10) ={1;2;5;10}

Mà x > 8 => x = 10

c)

Vì 126 chia hết cho x ѵà 210 chia hết cho x => x ∈ ƯC(126; 210)

Phân tích

126 = 2 ．3² ．7

210 = 2 ．3 ．5 ．7

ƯCLN(126; 210) = 2 ．3 ．7 = 42

ƯC(126; 210) = { 1; 2; 3; 6; 7; 14; 21; 42 }

Vì 15 < x < 30 => x = 21

a) \(B\left(14\right)=\left\{0;14;28;42;56;70;84;.......\right\}\)

Vì \(20< x< 8\Rightarrow x\in\left\{28;42;56;70\right\}\)

b) Vì 70 chia hết cho x và 80 chia hết cho x nên \(\Rightarrow x\inƯC\left(70;80\right)\)

Phân tích :

\(70=2.5.7\)

\(80=2^4.5\)

Mà \(x>8\Rightarrow x=10\)

c) Vì 126 chia hết cho x  và 210 chia hết cho x nên \(\Rightarrow x\inƯC\left(126;210\right)\)

Phân tích :

\(126=2.3^2.7\)

\(210=2.3.5.7\)

\(ƯC\left(126;210\right)=\left\{1;2;3;6;7;14;21;42\right\}\)

\(ƯCLN\left(126;210\right)=2.3.7=42\)

Theo đề : \(x\in\left(>15< 30\right)\Rightarrow x=21\)

a) 31x + (1+2+...+30) = 1240

   31x + 31.15 = 1240

  31x =1240 - 465

   31x = 775

   x= 25

b) (1+x) .x:2 = 210

  (x+1)x =210.2 = 21.20

 x =20

a)(x+x+...+x)+(1+2+...+30)=1240

31x+465=1240

31x=1240-465

31x=775

x=775/31

x=25

b)1+2+3+...+x=210

Đặt A=1+2+3+...+x

A có: (x-1)+1=x(số hạng)

A=(x+1)*x/2=210

(x+1)*x=210*2

(x+1)*x=420

=>x=20

a) \(x+\left(x+1\right)+......+\left(x+30\right)=1240\\ \Rightarrow31x+465=1240\\ \Rightarrow31x=775\\ \Rightarrow x=25\)

b) \(1+2+3+.........+x=210\\ \Rightarrow\frac{\left(x+1\right)x}{2}=210\\ \Rightarrow\left(x+1\right)x=420\\ \Rightarrow x=20\)

a)

x + (x + 1) + (x + 2) + ... + (x + 30) = 1240

x + x + 1 + x + 2 + ... + x + 30 = 1240

(x + x + ... + x) + (1 + 2 + ... + 30) = 1240

(x . [30 - 1 + 1 + 1]) + ([30 + 1] . [30 - 1 + 1] : 2) = 1240

31x + 465 = 1240

           31x = 1240 - 465

           31x = 775

                x = 775 : 31

                x = 25

b) 1 + 2 + 3 + ... + x = 210

(x + 1) . (x - 1 + 1) : 2 = 210

     (x + 1) . (x - 1 + 1) = 210 . 2

     (x + 1) . (x - 1 + 1) = 420

                   (x + 1) . x = 420

Mà 20 . 21 = 420 => x = 20

a)

x + (x + 1) + (x + 2) + ... + (x + 30) = 1240

x + x + 1 + x + 2 + ... + x + 30 = 1240

(x + x + ... + x) + (1 + 2 + ... + 30) = 1240

(x . [30 - 1 + 1 + 1]) + ([30 + 1] . [30 - 1 + 1] : 2) = 1240

31x + 465 = 1240

           31x = 1240 - 465

           31x = 775

                x = 775 : 31

                x = 25

b) 1 + 2 + 3 + ... + x = 210

(x + 1) . (x - 1 + 1) : 2 = 210

     (x + 1) . (x - 1 + 1) = 210 . 2

     (x + 1) . (x - 1 + 1) = 420

                   (x + 1) . x = 420

Mà 20 . 21 = 420 => x = 20