a) .(2+x)+(4+x)+(6+x)+.............+(52+x)=780
b). (1/15+1/35+1/63)*x=1
a / 1,5 . x + 15 + x = 31
b / ( x + 1 ) + ( x + 2 ) + ( x+ 3 ) + ( x +4 ) + ( x +5 ) = 45
c / 50 % . x + x = 52
d / x - 2/3 - 2/15 - 2/35 - 2/63 = 1/9
e / 75 / 20 - x =2/3 x 10
( Tìm x )
a) 1,5 . x + 15 + x = 31
(1,5 + 1) . x + 15 = 31
2,5 .x = 31 - 15
2,5 - x = 16
x = 2,5 - 16
x = -13,5
b) (x + 1) + (x + 2) + (x + 3) + ( x + 4) + (x + 5) = 45
(x + x + x ....+ x) + (1 + 2 + 3 + 4 + 5) = 45
5x + 15 = 45
5x = 45 - 15
5x = 30
x = 6
\(50\%.x+x=52\)
\(\frac{1}{2}x+x=52\)
\(x.\left(\frac{1}{2}+1\right)=52\)
\(x.\left(\frac{1}{2}+\frac{2}{2}\right)=52\)
\(x.\frac{3}{2}=52\)
\(x=52:\frac{3}{2}\)
\(x=52.\frac{2}{3}\)
\(x=\frac{104}{3}\)
Vậy \(x=\frac{104}{3}\)
\(x-\frac{2}{3}-\frac{2}{15}-\frac{2}{35}-\frac{2}{63}=\frac{1}{9}\)
\(x-\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}\right)=\frac{1}{9}\)
\(x-\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}\right)=\frac{1}{9}\)
\(x-\left(1-\frac{1}{9}\right)=\frac{1}{9}\)
\(x-1+\frac{1}{9}=\frac{1}{9}\)
\(x=\frac{1}{9}-\frac{1}{9}+1\)
\(x=1\)
Vậy \(x=1\)
\(\frac{75}{20}-x=\frac{2}{3}.10\)
\(x=\frac{75}{20}-\frac{20}{3}\)
\(x=\frac{225}{60}-\frac{400}{60}\)
\(x=-\frac{175}{60}=-\frac{35}{12}\)
Vậy \(x-\frac{35}{12}\)
Bài 2 : Tính
a) A= (1- 1/42) x (1-1/52) x (1-1/62) x ... x (1-1/2002)
b) B= 3/35 x 15/63 x 35/99 x ... x 9999/10815
Mình đag cần gấp
a) CÓ: A = (1-1/42).(1-1/52).(1-1/62)......(1-1/2002)
=\(\frac{4^2-1^2}{4^2}\). \(\frac{5^2-1^2}{5^2}\). \(\frac{6^2-1^2}{6^2}\)....... \(\frac{200^2-1^2}{200^2}\)
Ta có công thức sau : a2-b2= a2 -ab+ab-b2
= a(a-b) + b(a-b)
= (a+b)(a-b)
ÁP DỤNG CÔNG THỨC TRÊN VÀO BÀI TOÁN TA ĐƯỢC :
A= \(\frac{3.5}{4^2}\). \(\frac{4.6}{5^2}\). \(\frac{5.7}{6^2}\)......\(\frac{199.201}{200^2}\)
= \(\frac{\left(3.4.5.....199\right)\left(5.6.7....201\right)}{\left(4.5.6......200\right)^2}\)
= \(\frac{\left(3.4.5.......199\right)\left(5.6.7.....200.201\right)}{\left(4.5.6.....199.200\right)\left(4.5.6......200\right)}\)
= \(\frac{3.201}{200.4}\)
= \(\frac{603}{800}\)
b)Từ đề bài ta suy ra : B=\(\frac{1.3}{5.7}\).\(\frac{3.5}{7.9}\). \(\frac{5.7}{9.11}\)...... \(\frac{99.101}{103.105}\)
= \(\frac{1.3^2.5^2.7^2......99^2.101}{5.7^2.9^2.11^2....99^2.101^2.103^2.105}\)
=\(\frac{3^2.5}{101.103^2.105}\)
=\(\frac{3}{7500563}\)
A 2/3 + 2/15 + 2/35 + 2/63
B (1/15 + 1/35 + 1/63) x X =1
A=12/15 + 28/315
A=8/9
B. 1/9 x X = 1 X= 1: 1/9X= 9Tìm x : biết:
a, 48 x 0.5 : X = 150 ; b, ( X +1/3 ) x 3/4 - 1/2 = 5/6
c,3/4 : ( X - 1/2 ) +1/2 =2/3 ; d,(X+1)+(X+ 2)+(X+3)+...+(X+100)= 5550
e, (1/15+1/35+1/63+1/99) x X =4 ; f,1/3+1/6+1/10+...+1 2/X(X+1) = 2017/2019
a ) A = 1/3 + 1/15 + 1/35 + 1/63 + 1/99 + 1/143
b) x + ( x + 1 ) + ( x + 2 ) + ....+ ( x + 99 ) = 14950
éc ô éc
a) \(A=\dfrac{1}{3}+\dfrac{1}{5}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+\dfrac{1}{143}\)
\(A=\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+\dfrac{1}{7.9}+\dfrac{1}{9.10}+\dfrac{1}{143}\)
\(A=\dfrac{1}{2}.\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\right)+\dfrac{1}{143}\)
\(A=\dfrac{1}{2}.\left(1-\dfrac{1}{100}\right)+\dfrac{1}{143}=\dfrac{1}{2}.\dfrac{99}{100}+\dfrac{1}{143}=\dfrac{99}{200}+\dfrac{1}{143}=\dfrac{99.143+200.1}{200.143}=\dfrac{14157+200}{28600}=\dfrac{14357}{28600}\)
b) \(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+99\right)=14950\)
\(\Rightarrow x+x+...+x+\left(1+2+...+99\right)=14950\)
\(\Rightarrow100x+\left(\left(99+1\right):2\right).99:2=14950\)
\(\Rightarrow100x+2475=14950\Rightarrow100x=12475\Rightarrow x=\dfrac{12475}{100}=\dfrac{499}{4}\)
1/3+ 1/15 + 1/35 + 1/63 +...... + 1/(x+1)*(x+4) = 199/400 tìm x
\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{63}+...+\frac{1}{\left(x+1\right)\left(x+4\right)}=\frac{199}{400}\)(ĐK \(x\ne-1;-4\))
=> \(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+...+\frac{1}{\left(x+1\right)\left(x+4\right)}=\frac{199}{400}\)
=> \(\frac{1}{2}\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{\left(x+1\right)\left(x+4\right)}\right)=\frac{199}{400}\)
=> \(\frac{1}{2}\left(1-\frac{1}{x+4}\right)=\frac{199}{400}\)
=> \(1-\frac{1}{x+4}=\frac{199}{400}:\frac{1}{2}=\frac{199}{200}\)
=> \(\frac{1}{x+4}=1-\frac{199}{200}=\frac{1}{200}\)
=> x + 4 = 200 => x = 196(tm)
Ta có
1/3 = 1/1 x 3
1/15 = 1/3 x 5
1/35 = 1/5 x 7
.....
1/(x + 1 ) x ( x + 4 )
\(\Rightarrow\)1 - 1/3 + 1/3 - 1/5 +1/5 - 1/7 +............+ 1/( x + 1 ) - 1/( x + 4) = 199/400
\(\Rightarrow\)1 - 1/( x + 4 ) = 199/400
\(\Rightarrow\)1/(x + 4 ) = 1 - 199/400
\(\Rightarrow\)1/(x + 4 ) = 201/400
còn lại bạn tự làm nha
Tìm x
a,x/15=2/5
b,3/x-7=27/135
c,320.x-10=5.48:24
d,5.x-1952=2500-1947
e,(x+1)+(x+2)+(x+3)+(x+4)+(x+5)=45
f,x-2/3-2/15-2/35-2/63=1/9
g,(x-1.3/4).3/2.2+1/2-3/2=2
h,2/6+2/12+2/20+...+2/x.(x+14)=2013/2015
k,3+5+7+...+2015/2+4+6+...+2014+x=1
=a, \(\dfrac{x}{15}\) = \(\dfrac{2}{5}\)
= \(x.5=15.2\)
=> \(x=\dfrac{15.2}{5}\)\(=\dfrac{30}{5}\) \(=6\)
Vậy \(x=6\)
b, \(\dfrac{3}{x-7}\) \(=\dfrac{27}{135}\)
= \(\dfrac{3}{x-7}\) \(=\dfrac{3}{15}\)
= \(x-7=15\)
\(x=15+7\)
\(x=22\)
vậy x = 22
c, \(320.x-10=5.48:24\)
= \(320x-10=240:24\)
= \(320x-10=10\)
= \(320x=10+10\)
\(320x=20\)
\(x=20:320\)
\(x=0,0625\)
d, \(5x-1952=\) \(2500-1947\)
\(5x-1952=553\)
\(5x=553+1952\)
\(5x=2505\)
\(x=2505:5\)
\(x=501\)
e, \(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+\left(x+4\right)\left(x+5\right)=45\)
= \(\left(x+x+x+x+x\right)\)+\(\left(1+2+3+4+5\right)\) \(=45\)
= \(5x+15=45\)
\(5x=45-15\)
\(5x=30\)
\(x=30:5\)
\(x=6\)
f, \(x-\dfrac{2}{3}-\dfrac{2}{15}-\dfrac{2}{35}-\dfrac{2}{63}=\dfrac{1}{9}\)
= \(x-\dfrac{2}{3}-\dfrac{2}{15}-\dfrac{2}{35}=\dfrac{1}{9}+\dfrac{2}{63}\)
= \(x-\dfrac{2}{3}-\dfrac{2}{15}-\dfrac{2}{35}=\dfrac{1}{7}\)
= \(x-\dfrac{2}{3}-\dfrac{2}{15}=\dfrac{1}{7}+\dfrac{2}{35}\)
= \(x-\dfrac{2}{3}-\dfrac{2}{15}=\dfrac{1}{5}\)
= \(x-\dfrac{2}{3}=\dfrac{1}{5}+\dfrac{2}{15}\)
= \(x-\dfrac{2}{3}=\dfrac{1}{3}\)
\(x=\) \(\dfrac{1}{3}+\dfrac{2}{3}\)
\(x=1\)
k, \(\dfrac{3+5+7+...+2015}{2+4+6+...+2014+x}=1\)
ta thấy phần tử là tập hợp các số lẻ ; phần mẫu là tập hợp các số chẵn
mà số chẵn hơn số lẻ 1 đơn vị
nên x thuộc tổng các số phần tử hơn mẫu là 1 đơn vị
=> từ \(2+4+6+...+2014\)có số số hạng là :
( 2014 - 2 ) : 2 + 1 = 1007
vậy x sẽ bằng :
( 1 + 1 ) . 1007 : 2 = 1007
vập số cần tìm là : 1007
a,
x-2/3-2/15-2/35-2/63=1/9
b
(x+1
3)+(x+1/9)+(x+1/27)+(x+1/81)=56/81
c,
(1/3*5+1/5*7+1/7*9+.....+1/19*21)*x=9/7
d,3+5+7+...+2015/2+4+6+...+2016+x=1
e,2/6+2/12+2/20+...+2/x*(x+1)=2013/2015
Bài 2. Tìm các số tự nhiên x biết:
a) x:15, x:35, x:42 và 250 < x < 850 .
b) x là số nhỏ nhất khác 0 thoả mãn x:15 và x:115;
c) (x−1)52,(x−1) 35 và 1000 < x < 2000
a) \(x⋮15;x⋮35;x⋮42\&250< x< 850\) (sửa dấu chia thành chia hết)
\(BCNN\left(15;35;42\right)=210\)
\(\Rightarrow x\in BC\left(15;35;42\right)=\left\{0;210;420;630;840;...\right\}\)
mà \(250< x< 850\)
\(\Rightarrow x\in\left\{420;630;840\right\}\)
b) x nhỏ nhất khác 0 thỏa mãn \(x⋮15;x⋮115\)
\(BCNN\left(15;115\right)=345\)
Vậy \(x\in\left\{345\right\}\) thỏa mãn đề bài
phần c lỗi nha ạ, mình sửa lại
c) (x−1) chia hết 52,(x−1) chia hết 35 và 1000 < x < 2000