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a. x+(x+1)+(x+2)+...+(x+30)=1240
=> 31.x (gồm 30 số x trong các ngoặc và số x ở ngoài cùng) + (1+2+...+30)=1240
=> 31.x+\(\frac{\left(30+1\right).30}{2}\)=1240
=> 31.x+465=1240
=> 31.x=1240-465
=> 31.x=775
=> x=775:31
=> x=25.
b. => \(\frac{x.\left(x+1\right)}{2}=210\)
=> x.(x+1)=210.2
=> x.(x+1)=420
=> x.(x+1)=20.21
=> x.(x+1)=20.(20+1)
=> x=20.
a)
x+(x+1)+..+(x+30)=1240
=>x+x+x+..+x+(1+2+..+30)=1240
=>31.x+465=1240
=>31.x=775
=>x=25
a)
1+2+3+4+5+...+x=210
=>(x+1).x:2=210
=>(x+1).x=420
=>420=(x+1).x=(20+1).20
=>x=20
b) Ta có : \(\left(x-\frac{1}{3}\right)^2-\frac{1}{4}=0\)
\(\Rightarrow\left(x-\frac{1}{3}\right)^2=\frac{1}{4}\)
\(\Rightarrow\orbr{\begin{cases}\left(x-\frac{1}{3}\right)^2=\left(\frac{1}{2}\right)^2\\\left(x-\frac{1}{3}\right)^2=\left(-\frac{1}{2}\right)^2\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-\frac{1}{3}=\frac{1}{2}\\x-\frac{1}{3}=-\frac{1}{2}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{5}{6}\\x=-\frac{1}{6}\end{cases}}\)
b) \(\left(x-\frac{1}{3}\right)^2-\frac{1}{4}=0\)
\(\Leftrightarrow\left(x-\frac{1}{3}\right)^2=\frac{1}{4}\)
\(\Rightarrow\orbr{\begin{cases}x-\frac{1}{3}=\frac{1}{4}\\x-\frac{1}{3}=-\frac{1}{4}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{7}{12}\\x=\frac{1}{12}\end{cases}}\)
d) \(\frac{x+5}{2}=\frac{8}{x+5}\)
\(\Rightarrow\left(x+5\right)^2=16\)
\(\Rightarrow\orbr{\begin{cases}x+5=16\\x+5=-16\end{cases}\Rightarrow\orbr{\begin{cases}x=11\\x=-21\end{cases}}}\)
a)
\(x+\left(x-1\right)+\left(x-2\right)+...+\left(x-50\right)=255\\ x+x-1+x-2+...+x-50=255\\ \left(x+x+x+...+x\right)-\left(1+2+3+...+50\right)\\ 51x-1275=255\\ 51x=1530\\ x=30\)
e)
\(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+30\right)=1240\\ x+x+1+x+2+...+x+30=1240\\ \left(x+x+x+...+x\right)+\left(1+2+3+...+30\right)=1240\\ 31x+465=1240\\ 31x=775\\ x=25\)
f)
\(\left(x-1\right)+\left(x-2\right)+...+\left(x-19\right)+\left(x-20\right)=-610\\ x-1+x-2+...+x-19+x-20=-610\\ \left(x+x+x+...+x\right)-\left(1+2+3+...+20\right)=-610\\ 20x-210=-610\\ 20x=-400\\ x=-20\)
a)
Ta có: 5 = 2+3; 9 = 4+5 ; 13 = 6+7 ; 17 = 8+9;.....
Do vậy x = a + ( a + 1) ( a thuộc N )
Nên 1 + 5 + 9 + 13 + 16 + ....+ x = 1+2+3+4+5+6+7+.....+a+ ( a + 1 ) = 501501
Hay (a + 1)( a + 2) = 1003002 = 1001 . 1002
Suy ra : a = 1000
Do đó : x = 1000 + ( 1000+ 1) = 2001
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
a) x + [x + 1] + [x + 2] + ... + [x + 30] = 1240
=> 31 . x + (1 + 2 + 3 + 4 +...+ 29 + 30) = 1240
31 . x + 31.15 = 1240
31 . x = 1240 - 31.15
31 . x = 775
x = 775 : 31
x = 25
b) 1 + 2 + 3 + ... + x = 210
=< x . (x + 1) = 201 . 2
=> x . (x + 1) = 420
Vì 420 = 20 . 21 nên 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 + 30 ) = 1240
=> ( x + ... + x ) + ( 1 + 2 + ... + 30 ) = 1240
=> 31 x + 465 = 1240
=> 31 x = 775
=> x = 25.
b) 1 + 2 + 3 + ... + x = 210
=> ( x + 1 ) . [ ( x - 1 ) : 1 + 1 ] : 2 = 210
=> ( x + 1 ) . x = 420
=> ( x + 1 ) . x = 21 . 20
=> x = 20
a) x+(x+1)+...+(x+30)=1240
(x+...+x)+(1+2+...+30)=1240
31x+465=1240
31x=775
x=25
b) 1+2+3+...+x=210
(x+1).[(x-1):1+1]:2=210
(x+1).x=420
(x+1).x=21.20
x = 20.