Tính nhanh:
20092009x200820082008-200920092009x20082008
Tìm x:
(x-7)+x=5
2x-7=5-x
Chứng tỏ:
1/31 + 1/32 + ... + 1/90 > 5/6
Chứng tỏ:
1/31+1/32+...+1/90>5/6
Nhanh lên mình tích cho
Xếp lại một tí: Tổng S = 1/31+1/90 +1/32+1/89 .....+1/60*1/61. (có 30 cặp cả thẩy).
Tiếp : S = (31+90)/31*90 + (32+89)/32*89..+(60+61)/(60*61)
S = 121 {1/(31.90) +1/(32.89) .....1/(60.61)} (30 số hạng)
Thấy tiếp 1/(60.61) nhỏ nhất trong các số hạng trong ngoặc) nên ta chỉ xét tổng So bằng cách thay các số hạng của S bằng 121/(60.61). Khi đó tổng mới có 30 số hạng được tính là
So = 30 * 121/(60.61) = 121/122.
Vậy So = 121/122 lớn hơn 5/6. Mà S>So nên suy ra ĐPCM.
Chứng tỏ : 31/2 x 32/2 x 33/2 x .... x 60/2 = 1 x 3 x 5 x ... x 59
Chứng tỏ : 31/2 x 32/2 x 33/2 x .... x 60/2 = 1 x 3 x 5 x ... x 59
Làm đúng thì tick!
\(=\frac{31\times32\times...\times60}{2\times2\times...\times2}=\frac{31\times32\times...\times60}{2^{30}}\)
\(=\frac{\left(31\times32\times...\times60\right)\times\left(1\times2\times...\times30\right)}{2^{30}\times\left(1\times2\times...\times30\right)}\)
\(=\frac{32\times32\times...\times60\times1\times2\times...\times30}{\left(2\times1\right)\left(2\times2\right)\times...\times\left(2\times30\right)}\)
\(=\frac{\left(1\times3\times...\times59\right)\left(2\times4\times...\times60\right)}{\left(2\times4\times...\times60\right)}=1\times3\times...\times59\)
=>Đpcm
bài 7
4x3 + 12 = 120
b, ( x - 4 )2 = 64
c, ( x + 1 )3 - 2 = 52
d, 136 - ( x + 5)2 = 100
e, 4x = 16
f, 7x. 3 - 147 = 0
g, 2x+3 - 15 = 17
h, 52x-4. 4 = 102
i, (32 - 4x)(7 - x) = 0
k, ( 8 - x)(10 - 2x) = 0
m, 3x + 3x+1 = 108
n, 5x+2 + 5x+1 = 750
a: \(4x^3+12=120\)
=>\(4x^3=108\)
=>\(x^3=27=3^3\)
=>x=3
b: \(\left(x-4\right)^2=64\)
=>\(\left[{}\begin{matrix}x-4=8\\x-4=-8\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=12\\x=-4\end{matrix}\right.\)
c: (x+1)^3-2=5^2
=>\(\left(x+1\right)^3=25+2=27\)
=>x+1=3
=>x=2
d: 136-(x+5)^2=100
=>(x+5)^2=36
=>\(\left[{}\begin{matrix}x+5=6\\x+5=-6\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=-11\end{matrix}\right.\)
e: \(4^x=16\)
=>\(4^x=4^2\)
=>x=2
f: \(7^x\cdot3-147=0\)
=>\(3\cdot7^x=147\)
=>\(7^x=49\)
=>x=2
g: \(2^{x+3}-15=17\)
=>\(2^{x+3}=32\)
=>x+3=5
=>x=2
h: \(5^{2x-4}\cdot4=10^2\)
=>\(5^{2x-4}=\dfrac{100}{4}=25\)
=>2x-4=2
=>2x=6
=>x=3
i: (32-4x)(7-x)=0
=>(4x-32)(x-7)=0
=>4(x-8)*(x-7)=0
=>(x-8)(x-7)=0
=>\(\left[{}\begin{matrix}x-8=0\\x-7=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=8\\x=7\end{matrix}\right.\)
k: (8-x)(10-2x)=0
=>(x-8)(x-5)=0
=>\(\left[{}\begin{matrix}x-8=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=5\end{matrix}\right.\)
m: \(3^x+3^{x+1}=108\)
=>\(3^x+3^x\cdot3=108\)
=>\(4\cdot3^x=108\)
=>\(3^x=27\)
=>x=3
n: \(5^{x+2}+5^{x+1}=750\)
=>\(5^x\cdot25+5^x\cdot5=750\)
=>\(5^x\cdot30=750\)
=>\(5^x=25\)
=>x=2
Bài tập 6:Tính nhanh
A) 3/4 + 2/5 + 1/4 + 3/5 =....
B) 2/3 x 3/4 x 4/5 x 5/6 =...
C) 4/5 x 3/7 + 4/5 x 4/7 =...
D) 2/5 x 7/4 - 2/5 x 3/7 =...
E) 75/100 + 18/21 + 19/32 + 1/4 +3/21 + 13/32 =....
ai lam to tick cho
Cho m= 3/5 x (6/7 x 8/9 x 10/11 x ... x 32/33) và N = 5/6 x 7/8 x 9/10 x ... x 31/32
đề bài là làm gì vậy bạn?
Tính m x n nhé bạn
1) Tìm x biết:
a)52x-3-2.52=3.52
b)3x-7=x=3
c)(x+1)+(x+3)+(x+5)+...+(x+99)=0
Tính nhanh:
(6x5+7-37)x(1+2+3+4+5+6+7+8+9+10)
=(30+7-37)*(1+2+3+4+5+6+7+8+9+10)
=0*(1+2+3+4+5+6+7+8+9+10)
=0
( 6 x 5 + 7 - 37)x (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 +9 + 10)
0 x 55 = 0
tính nhanh
4/5-2/3/+1/5-1/3
2/5 x 7/4 - 2/5x3/7
13/4 x 2/3 x 4/13 x 3/12
75/100 + 18/21 + 19/32 +1/4 + 3/21 + 13/32
2/5 + 6/9+3/4+3/5+1/3+1/4
Bài giải
a, \(\frac{4}{5}-\frac{2}{3}+\frac{1}{5}-\frac{1}{3}\)
\(=\left(\frac{4}{5}+\frac{1}{5}\right)-\left(\frac{2}{3}+\frac{1}{3}\right)=1-1=0\)
b, \(\frac{2}{5}\text{ x }\frac{7}{4}-\frac{2}{5}\text{ x }\frac{3}{7}\)
\(=\frac{2}{5}\text{ x }\left(\frac{7}{4}-\frac{3}{7}\right)=\frac{2}{5}\text{ x }\frac{37}{28}=\frac{37}{70}\)
c, \(\frac{13}{4}\text{ x }\frac{2}{3}\text{ x }\frac{4}{13}\text{ x }\frac{3}{12}=\frac{13\text{ x }2\text{ x }4\text{ x }3}{4\text{ x }3\text{ x }13\text{ x }12}=\frac{1}{6}\)
d, \(\frac{75}{100}+\frac{18}{21}+\frac{19}{32}+\frac{1}{4}+\frac{3}{21}+\frac{13}{32}\)
\(=\frac{3}{4}+\frac{18}{21}+\frac{19}{32}+\frac{1}{4}+\frac{3}{21}+\frac{13}{32}\)
\(=\left(\frac{3}{4}+\frac{1}{4}\right)+\left(\frac{18}{21}+\frac{3}{21}\right)+\left(\frac{19}{32}+\frac{13}{32}\right)\)
\(=1+1+1\)
\(=3\)
e, \(\frac{2}{5}+\frac{6}{9}+\frac{3}{4}+\frac{3}{5}+\frac{1}{3}+\frac{1}{4}\)
\(=\frac{2}{5}+\frac{2}{3}+\frac{3}{4}+\frac{3}{5}+\frac{1}{3}+\frac{1}{4}\)
\(=\frac{1}{5}\left(2+3\right)+\frac{1}{3}\left(2+1\right)+\frac{1}{4}\left(3+1\right)\)
\(=\frac{1}{5}\cdot5+\frac{1}{3}\cdot3+\frac{1}{4}\cdot4\)
\(=1+1+1\)
\(=3\)
a, \(\frac{4}{5}-\frac{2}{3}+\frac{1}{5}-\frac{1}{3}\)
\(=\left(\frac{4}{5}+\frac{1}{5}\right)-\left(\frac{2}{3}+\frac{1}{3}\right)=1-1=0\)
b, \(\frac{2}{5}\text{ x }\frac{7}{4}-\frac{2}{5}\text{ x }\frac{3}{7}\)
\(=\frac{2}{5}\text{ x }\left(\frac{7}{4}-\frac{3}{7}\right)=\frac{2}{5}\text{ x }\frac{37}{28}=\frac{37}{70}\)
c, \(\frac{13}{4}\text{ x }\frac{2}{3}\text{ x }\frac{4}{13}\text{ x }\frac{3}{12}=\frac{13\text{ x }2\text{ x }4\text{ x }3}{4\text{ x }3\text{ x }13\text{ x }12}=\frac{1}{6}\)
d, \(\frac{75}{100}+\frac{18}{21}+\frac{19}{32}+\frac{1}{4}+\frac{3}{21}+\frac{13}{32}\)
\(=\frac{3}{4}+\frac{18}{21}+\frac{19}{32}+\frac{1}{4}+\frac{3}{21}+\frac{13}{32}\)
\(=\left(\frac{3}{4}+\frac{1}{4}\right)+\left(\frac{18}{21}+\frac{3}{21}\right)+\left(\frac{19}{32}+\frac{13}{32}\right)\)
\(=1+1+1\)
\(=3\)
e, \(\frac{2}{5}+\frac{6}{9}+\frac{3}{4}+\frac{3}{5}+\frac{1}{3}+\frac{1}{4}\)
\(=\frac{2}{5}+\frac{2}{3}+\frac{3}{4}+\frac{3}{5}+\frac{1}{3}+\frac{1}{4}\)
\(=\frac{1}{5}\left(2+3\right)+\frac{1}{3}\left(2+1\right)+\frac{1}{4}\left(3+1\right)\)
\(=\frac{1}{5}\cdot5+\frac{1}{3}\cdot3+\frac{1}{4}\cdot4\)
\(=1+1+1\)
\(=3\)
a , =(4/5+1/5)-(2/3+1/3)=1-1=0
b , =2/5 x (7/4-3/7) =2/5 x 37/28 =74/140=37/70
c, =13/4 x 2/3 x 13/4 x 2/3=26/12 x 26/12= 13/6 x 13/6 =13 x 13/6 x 6(gạch 13 trên tử thì tử còn 1 x 13,mẫu hết.) =1 x 13/1=13
d, =3/4+6/7+19/32 +1/4+1/7 +13/32=(3/4+1/4 )+(6/7+1/7)+(19/32+13/32)=1+1+1=3
e, =(2/5+3/5)+(2/3+1/3)+(3/4+1/4) [6/9 rút gọn thành 2/3] =1+1+1=3