x+{x+1}=2+4+6+8+10+....+100
A= 1/2 x 4 + 1/4 x 6 + 1/6 x 8 +1/8 x 10 + ... +1/98 x 100
2A=2/2x4+2/4x6+..+2/98x100
=> 2A=1-1/4+1/4-1/6+..+1/98-1/100
=> 2A=1-1/100
=> 2A=99/100
=> A=99/100:2
=> A=99/200
1. TÌM X :
10+3.(x-6)=5^10:5^8
2.TÍNH
A,100-[150-8.(7-4)^2]
B,(-999)+[(-23)+999]-[10-(-67)]
Bài 1:
$10+3(x-6)=5^{10}:5^8=5^2=25$
$3(x-6)=25-10=15$
$x-6=15:3=5$
$x=5+6=11$
Bài 2:
a. $100-[150-8(7-4)^2]=100-(150-8.3^2)=100-150+8.3^2$
$=-50+72=72-50=22$
b. $=-999-23+999-10-67=(-999+999)-10-(67+23)$
$=0-10-90=-(10+90)=-100$
BÀI 1 - Tính
a (0,8)^5/(0,4)^6
b 8^10+4^10/8^4+4^11
BÀI 2 - Tìm x ϵ Z
a 2^x-1 = 16
b (x-1)^2 = 25
c (x-1)^x+2 = (x-1)^x+6
d (x+20)^100 + I y+4 I = 0
Bài 1:
a)\(\frac{\left(0,8\right)^5}{\left(0,4\right)^6}=\frac{\left(0,2\cdot4\right)^5}{\left(0,2\cdot2\right)^6}=\frac{\left(0,2\right)^5\cdot\left(2^2\right)^5}{\left(0,2\right)^6\cdot2^6}=\frac{\left(0,2\right)^5\cdot2^{10}}{\left(0,2\right)^6\cdot2^6}=\frac{2^4}{0,2}=\frac{16}{\frac{2}{10}}=80\)
b)\(\frac{8^{10}+4^{10}}{8^4+4^{11}}=\frac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}=\frac{2^{30}+2^{20}}{2^{12}+2^{22}}=\frac{2^{20}\left(2^{10}+1\right)}{2^{12}\left(1+2^{10}\right)}=\frac{2^{20}}{2^{12}}=256\)
Bài 2:
a)\(2^{x-1}=16\)
\(\Rightarrow2^{x-1}=2^4\)
\(\Rightarrow x-1=4\Rightarrow x=5\)
b)\(\left(x-1\right)^2=25\)
\(\Rightarrow\left(x-1\right)^2=5^2=\left(-5\right)^2\)
\(\Rightarrow x-1=5\) hoặc \(x-1=-5\)
\(\Rightarrow x=6\) hoặc \(x=-4\)
Vậy \(x=6\) hoặc \(x=-4\)
c)\(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+6}\)
\(\Rightarrow\left(x-1\right)^{x+2}-\left(x-1\right)^{x+6}=0\)
\(\Leftrightarrow\left(x-1\right)^{x+2}\left[1-\left(x-1\right)^4\right]\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}\left(x-1\right)^{x+2}=0\\1-\left(x-1\right)^4=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x-1=0\\1=\left(x-1\right)^4\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=1\\\left(x-1\right)^4=\left(-1\right)^4=1^4\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=1\\x-1=1\\x-1=-1\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=1\\x=2\\x=0\end{array}\right.\)
d)\(\left(x+20\right)^{100}+\left|y+4\right|=0\left(1\right)\)
Ta thấy: \(\begin{cases}\left(x+20\right)^{100}\ge0\\\left|y+4\right|\ge0\end{cases}\)
\(\Rightarrow\left(x+20\right)^{100}+\left|y+4\right|\ge0\left(2\right)\)
Từ (1) và (2) suy ra \(\begin{cases}\left(x+20\right)^{100}=0\\\left|y+4\right|=0\end{cases}\)
\(\Rightarrow\begin{cases}x+20=0\\y+4=0\end{cases}\)\(\Rightarrow\begin{cases}x=-20\\y=-4\end{cases}\)
Tìm x thuộc N biết
a) 2x + 10 + 20
b) 123x + 877x =2000
c) 2x . ( x -10 ) = 0
d) 6 . ( x + 2 ) - ( 4x + 10 ) = 100
e) x . ( x + 1 ) = 2 + 4 + 6 + 8 + ....+ 2500
g) ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + .....+ ( x + 100 ) =5750
a) \(???\)
b) \(123x+877x=2000\)
\(1000x=2000\)
\(x=2000:1000\)
\(x=2\)
c) \(2x.\left(x-10\right)=0\)
=> \(x-10=0\)
\(x=10\)
d)\(6.\left(x+2\right)-\left(4x+10\right)=100\)
\(6.x+12-4x+10=100\)
\(2x+2=100\)
\(2x=98\)
\(x=98:2\)
\(x=49\)
e) \(x.\left(x+1\right)=2+4+6+8+...+2500\)
\(x.\left(x+1\right)=1563750\)
mà ta thấy : \(1250.1251=1563750\)
=> \(x=1250\)
g)\(\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=5750\)
\(x.100+5050=5750\)
\(x.100=5750-5050\)
\(x.100=700\)
\(x=7\)
1/ -8+13-...+x=250
2/ 1-3+5-7+...-x=-600
3/ -2+4-6+8-...+x=100
4/ 2-6=10-14+...-x=-800
giúp mình với nha
Tìm x biết
1/-8+13-...+x=205
2/1-3+5-7+...-x=-600
3/-2+4-6+8-...+x=100
4/2-6+10-14+...-x=-800
2/ 1 - 3 + 5 - 7 + ... + (x-2) - x = -600
=> ( - 2 ) + ( - 2 ) + .... + ( - 2 ) = - 600 ( số số hạng các số - 2 là A )
=> ( - 2 ) . A = - 600 => A = 300
Mặt Khác số số hạng ở dãy trên = ( x - 1 ) : 2 + 1 ( 1 )
Số số cặp = Số số hạng : 2 = 300 => Số số hạng = 600
Thay vào ( 1 ) Ta có :
( x - 1 ) : 2 + 1 = 600 => ( x - 1 ) : 2 = 599 => x = 599 . 2 + 1 = 1198+ 1 = 1199
Các câu 1,3,4 làm tương tự
Tìm x biết
a) 1-4+7-10+...-x=-75
b) -1+3-5+7-...+x=1000
c) -2=4-6+8-...+x=100
d) 2-6+10-14+...-x=-800
A, X = 2 x 10 000 + 2 x 1000 +5 x 100+9 x 10+7
B, X =7 x 100 000 + 7 x 10 000 + 8 x 100 + 5
C, X= 4 x 10 000 +6 x 100 + 3 x 10
D, X= 1 x 100 000 + A x 1000 + 2 x100 + 1 x 10 + B
MONG CAC BAN LAM GIUP MINH
x + (-3) + (-10) + (-105) = -161
và x + (-1) + ( -2) + (-3) ........(-100)= -5053
và x + (-2) + (-4) + (-6) + (-8) .......+(-100)= -612