a: =>2x-x=-5/2-1/3

=>x=-17/6

b: =>4(x-2)²=36

=>(x-2)²=9

=>x-2=3 hoặc x-2=-3

hay x=5 hoặc x=-1

c: =>2x+1/2=5/6

=>2x=1/3

hay x=1/6

a: =>2x-x=-5/2-1/3

=>x=-17/6

b: =>4(x-2)²=36

=>(x-2)²=9

=>x-2=3 hoặc x-2=-3

hay x=5 hoặc x=-1

c: =>2x+1/2=5/6

=>2x=1/3

hay x=1/6

(x - 1) + (x - 2) + (x - 3) + ⋯ + (x - 50) = 1225

x-1+x-2+x-3+....+x-50=1225

50x-(1+2+3+...+50)=1225

50x-1275=1225

50x=1225+1275

50x=2500

x=2500:50

x=50

50x là 50 nhân x đó nha bạn

(x-1)+(x-2)+...+(x-50)=1225

(x+x+x+...+x)-(1+2+3+4+...+50)=1225

(x*50)-1275=1225

x*50=1225+1275

x=2500:50

x=50

Có 1+2+3+...+x=\(\left(1+x\right)\times x:2=1225\)

\(\Rightarrow\left(1+x\right)\times x=1225\times2=2450\)

mà 49x50=2450

nên X(X+1)=49x50

\(\Rightarrow\)X=49

dãy trên có số số hạng là:

(1225-1):1+1=1225 số

tổng là:

(1225+1)nhân 1225 :2=750925

\(P=\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{6}\right)\left(1-\dfrac{1}{10}\right)...\left(1-\dfrac{1}{1225}\right)\left(1-\dfrac{1}{1275}\right)\)

\(=\dfrac{2}{3}.\dfrac{5}{6}.\dfrac{9}{10}...\dfrac{1224}{1225}.\dfrac{1274}{1275}\)

\(=\dfrac{2.2}{3.2}.\dfrac{5.2}{6.2}.\dfrac{9.2}{10.2}...\dfrac{1224.2}{1225.2}.\dfrac{1274.2}{1275.2}\)

\(=\dfrac{4}{9}.\dfrac{10}{12}.\dfrac{18}{20}...\dfrac{2448}{2450}.\dfrac{2548}{2550}\)

\(=\dfrac{1.4}{2.3}.\dfrac{2.5}{3.4}.\dfrac{3.6}{4.5}...\dfrac{48.51}{49.50}.\dfrac{49.52}{50.51}\)

\(=\dfrac{1.2.3...48.49}{2.3.4...49.50}.\dfrac{4.5.6...51.52}{3.4.5...50.51}\)

\(=\dfrac{1}{50}.\dfrac{52}{3}\)

\(=\dfrac{26}{75}\).

1) 1 + 2 + 3 + ... + x = 1225

=> (1 + x).x:2 = 1225

=> (1 + x).x = 1225.2

=> (1 + x).x = 2450

=> (1 + x).x = 50.49 = (-49).(-50)

Vậy \(x\in\left\{50;-49\right\}\)

2) 2 + 4 + 6 + ... + 2x = 210

=> 2.(1 + 2 + 3 + ... + x) = 210

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

=> (1 + x).x = 15.14 = (-14).(-15)

Vậy \(x\in\left\{15;-14\right\}\)

a)

\(1+2+......+x=1225\)

\(\Rightarrow\frac{\left(x+1\right)x}{2}=1225\)

\(\Rightarrow\left(x+1\right)x=2450\)

\(\Rightarrow\left(x+1\right)x=49.50\)

=> x = 49

Vậy x = 49

b)

\(2+4+....+2x=210\)

\(\Rightarrow2\left(1+2+....+x\right)=210\)

\(\Rightarrow2.\frac{\left(x+1\right)x}{2}=210\)

\(\Rightarrow x\left(x+1\right)=210\)

\(\Rightarrow x\left(x+1\right)=210\)

\(\Rightarrow x\left(x+1\right)=14.15\)

=> x = 14

Vậy x = 14

1) 1 + 2 + 3 +..... + X = 1225

Đặt A= 1 + 2 + 3 +..... + X 

Tổng A có số số hạng theo x là:

\(\left(x-1\right):1+1=x\) (số)

 Tổng A theo x là:

\(\left(x+1\right)\cdot x:2=\frac{x^2+x}{2}\)

Thay A vào ta đc:

\(\frac{x^2+x}{2}=1225\)\(\Leftrightarrow x^2+x-2450=0\)

\(\Leftrightarrow x^2-49x+50x-2450=0\)

\(\Leftrightarrow x\left(x-49\right)+50\left(x-49\right)=0\)

\(\Leftrightarrow\left(x-49\right)\left(x+50\right)=0\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x=49\left(tm\right)\\x=-50\left(loai\right)\end{array}\right.\) 

2)Đặt B= 2 + 4 + 6 +........ + 2X

Tổng B có số số hạng theo x là:

\(\left(2x-2\right):2+1=x\) (số)

Tổng B theo x là:

\(\left(2x+2\right)\cdot x:2=x^2+x\)

Thay B vào ta dc:

\(x^2+x=210\)\(\Leftrightarrow x^2+x-210=0\)

\(\Leftrightarrow x^2-14x+15x-210=0\)

\(\Leftrightarrow x\left(x-14\right)+15\left(x-14\right)=0\)

\(\Leftrightarrow\left(x+15\right)\left(x-14\right)=0\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x=14\left(tm\right)\\x=-15\left(loai\right)\end{array}\right.\)