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Tính tổng dãy dấu ngoặc trước
Đặt \(S=1\cdot2+2\cdot3+3\cdot4+...+98\cdot99\)
\(3S=1\cdot2\cdot3+2\cdot3\cdot(4-1)+...+98\cdot99\cdot(100-97)\)
\(3S=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot3\cdot4+...+98\cdot99\cdot100-97\cdot98\cdot99\)
\(3S=98\cdot99\cdot100\Rightarrow S=\frac{1}{3}\cdot98\cdot99\cdot100\)
Thay vào đề bài,ta có :
\(\frac{\frac{1}{3}\cdot98\cdot99\cdot100\cdot x}{26950}=12\frac{6}{7}:\frac{-3}{2}\)
\(\Leftrightarrow\frac{\frac{1}{3}\cdot98\cdot99\cdot100\cdot x}{26950}=12\frac{6}{7}\cdot\frac{2}{-3}\)
\(\Leftrightarrow\frac{\frac{1}{3}\cdot98\cdot99\cdot100\cdot x}{26950}=\frac{90}{7}\cdot\frac{2}{-3}\)
\(\Leftrightarrow\frac{\frac{1}{3}\cdot98\cdot99\cdot100\cdot x}{26950}=\frac{-30}{7}\cdot\frac{2}{-1}\)
\(\Leftrightarrow\frac{\frac{1}{3}\cdot98\cdot99\cdot100\cdot x}{26950}=\frac{-60}{-7}=\frac{60}{7}\)
\(\Leftrightarrow\frac{1}{3}\cdot98\cdot99\cdot100\cdot x=\frac{60}{7}\cdot26950\)
\(\Leftrightarrow\frac{1}{3}\cdot98\cdot99\cdot100\cdot x=231000\)
\(\Leftrightarrow323400\cdot x=231000\)
\(\Leftrightarrow x=231000:323400=\frac{5}{7}\)
Tử thần sai từ dòng:
\(\frac{\frac{1}{3}.98.99.100.x}{26950}=\frac{30}{7}.\frac{2}{-1}\Leftrightarrow12x=-\frac{60}{7}\Leftrightarrow x=\frac{-5}{7}\)
1)\(79-5\left(11-x\right)=34\)
\(\Rightarrow79-55+5x=34\)
\(\Rightarrow24+5x=34\)
\(\Rightarrow5x=-10\)
\(\Rightarrow x=-2\)
Vậy \(x=-2\)
2)\(32+2\left(7-x\right)=40\)
\(\Rightarrow32+14-2x=40\)
\(\Rightarrow46-2x=40\)
\(\Rightarrow2x=6\)
\(\Rightarrow x=3\)
Vậy \(x=3\)
3)\(\left(166-2x\right).8^9=2.8^{11}\)
\(\Rightarrow\left(83-x\right).2.8^9=2.8^{11}\)
\(\Rightarrow83-x=8^3\)
\(\Rightarrow83-x=512\)
\(\Rightarrow x=-429\)
Vậy \(x=-429\)
4)\(5^2.x-2^3.x=51\)
\(\Rightarrow x\left(5^2-2^3\right)=51\)
\(\Rightarrow x\left(25-8\right)=51\)
\(\Rightarrow17x=51\)
\(\Rightarrow x=3\)
Vậy \(x=3\)
5)\(3^x+4.3^x=5.3^7\)
\(\Rightarrow3^x\left(1+4\right)=5.3^7\)
\(\Rightarrow5.3^x=5.3^7\)
\(\Rightarrow3^x=3^7\)
\(\Rightarrow x=7\)
Vậy \(x=7\)
6)\(7.2^x-2^x=6.32\)
\(\Rightarrow2^x\left(7-1\right)=6.2^5\)
\(\Rightarrow6.2^x=6.2^5\)
\(\Rightarrow2^x=2^5\)
\(\Rightarrow x=5\)
Vậy \(x=5\)
7)\(15^{3-x}=225\)
\(\Rightarrow15^{3-x}=15^2\)
\(\Rightarrow3-x=2\)
\(\Rightarrow x=1\)
Vậy \(x=1\)
8)\(4.5^x-3=97\)
\(\Rightarrow4.5^x=100\)
\(\Rightarrow5^x=25\)
\(\Rightarrow5^x=5^2\)
\(\Rightarrow x=2\)
Vậy \(x=2\)
9)\(171-3.2^x=123\)
\(\Rightarrow3.2^x=48\)
\(\Rightarrow2^x=16\)
\(\Rightarrow2^x=2^4\)
\(\Rightarrow x=4\)
Vậy \(x=4\)
10)\(180-4.x^5=32\)
\(\Rightarrow4.x^5=148\)
\(\Rightarrow x^5=37\)//Đề có lỗi không ???
\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\right).x=\frac{23}{45}\)
\(\frac{1}{2}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{8.9.10}\right).x=\frac{23}{45}\)
\(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right).x=\frac{23}{45}\)
\(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{9.10}\right).x=\frac{23}{45}\)
\(\frac{1}{2}.\frac{22}{45}.x=\frac{23}{45}\)
\(\frac{11}{45}.x=\frac{23}{45}\)
\(x=\frac{23}{45}:\frac{11}{45}\)
\(x=\frac{23}{11}\)
\(a,67\times153-53\times67+712:8\)
\(=67\times\left(153-53\right)+\left(712:8\right)\)
\(=67\times100+89\)
\(=6700+89\)
\(=6789\)
\(b,168-\left\{5\times\left[143-\left(15-12\right)^2\right]+10\right\}:10\)
\(=168-\left\{5\times\left[143-3^2\right]+10\right\}:10\)
\(=168-\left\{5\times134+10\right\}:10\)
\(=168-\left\{670+10\right\}:10\)
\(=168-680:10\)
\(=168-68\)
\(=100\)
\(c,\left(-13\right)+84+\left(-87\right)+16\)
\(=13+84-87+16\)
\(=\left(13+87\right)-\left(84+16\right)\)
\(=100-100\)
\(=0\)
\(d,9-\left(12-15\right)\)
\(=9-\left(-3\right)\)
\(=12\)
a) \(22\frac{1}{2}\cdot\frac{7}{9}+50\%-1,25\)
\(=\frac{45}{2}\cdot\frac{7}{9}+\frac{50}{100}-\frac{125}{100}\)
\(=\frac{5}{2}\cdot\frac{7}{1}+\frac{1}{2}-\frac{5}{4}\)
\(=\frac{35}{2}+\frac{1}{2}-\frac{5}{4}=18-\frac{5}{4}=\frac{67}{4}\)
b) \(1,4\cdot\frac{15}{49}-\left(\frac{4}{5}+\frac{2}{3}\right):2\frac{1}{5}\)
\(=\frac{7}{5}\cdot\frac{15}{49}-\frac{22}{15}:\frac{11}{15}\)
\(=\frac{1}{1}\cdot\frac{3}{7}-\frac{22}{15}\cdot\frac{15}{11}\)
\(=\frac{3}{7}-2=\frac{3-14}{7}=\frac{-11}{7}\)
c) \(\left(-\frac{1}{2}\right)^2-\frac{7}{16}:\frac{7}{4}+75\%\)
\(=\frac{1}{4}-\frac{7}{16}\cdot\frac{4}{7}+\frac{75}{100}\)
\(=\frac{1}{4}-\frac{1}{4}+\frac{3}{4}=\frac{3}{4}\)
Bài 2 Bạn tự làm nhé
1.a,\(22\frac{1}{2}.\frac{7}{9}+50\%-1,25\)
\(=\frac{45}{2}.\frac{7}{9}+\frac{1}{2}-\frac{5}{4}\)
\(=\frac{35}{2}+\frac{1}{2}-\frac{5}{4}\)
\(=\frac{67}{4}\)
b,Các phép tính khác làm tương tự
Đổi các số ra hết thành phân số,có ngoặc thì lm ngoặc trc,Xoq đến nhân chia trước dồi mới cộng trừ
c,tương tự
2.
a,\(1\frac{3}{5}+\frac{7}{12}\div x=\frac{-9}{4}\)
\(\frac{8}{5}+\frac{7}{12}\div x=\frac{-9}{4}\)
\(\frac{7}{12}\div x=\frac{-77}{20}\)
Đến đây dễ bạn tự làm
b,\(\left(2\frac{4}{5}.x+50\right)\div\frac{2}{3}=-51\)
\(\left(\frac{14}{5}x+50\right)\div\frac{2}{3}=-51\)
\(\frac{14}{5}x+50=-34\)
\(\frac{14}{5}x=-84\)
Tự làm tiếp
c,\(\left|\frac{3}{4}.x-\frac{1}{2}\right|=\frac{1}{4}\)\(\Rightarrow\left|\frac{3}{4}x-\frac{1}{2}\right|=\varnothing\)
Bài 2:
a; 17 - 11 - (-39)
= 17 - 11 + 39
= 6 + 39
= 45
b; 125 - 4[ 3 -7 .(-2)]
= 125 - 4.[3 + 14]
= 125 - 4.17
= 125 - 68
= 57
bài1:a
-3 + 12
= 12 - 3
= 9
b)(-24) : 8 = -3
c)-9 - 13
= -9 + (-13)
=-(9 + 13)
= -22
Bài 1 :
a) (x-15 ) .32 = 32
<=> (x - 15 ) = 1
<=> x = 1 + 15
<=> x = 16
Vậy x = 90
b) ( x- 15 ) - 75 = 0
<=> x- 15 = 75
<=> x = 75 + 15
<=> x = 90
Vậy x= 90
c) 315 +(125 - x ) =435
<=> 125 -x = 435 - 315
<=> 125 - x = 120
<=> x = 125 - 120
<=> x = 5
Vậy x = 5
d) (x-78 ) . 2020 = 0
<=> x- 78 = 0
<=> x = 0 + 78
<=> x = 78
Vậy x = 78
e) 219 - 7. ( x + 1 )= 0
<=> 7.(x + 1 ) = 219
<=> 7x + 7 = 219
<=> 7x = 212
<=> x = 212 /7 ( L )
Vậy x \(\in\varnothing\)
g) 3x .3 = 243
<=> 3 x = 81
<=> 3x = 34
<=> x = 4
Vậy x = 4
Phần h) bạn làm tương tự
Bài 2 :
Mình đang làm ,lát mình làm xong rồi gửi,tầm 4:30 h gì đó ,vì mình đang học trực tuyến !
bài 2 :
a) Ta có : 2161 > 2160 = (24 )40 =1640 > 1340
Vậy 1340 < 2161
b) 10249 = (210)9 = 2 90
2100 = 2100
=> ta thấy 290 < 2100 => 10249 < 2100
c) tương tự d) nha bạn ,thực ra mình làm d) trước
d) 48 . ( 4 + 8 ) = 48 . 12 = 576
43 + 83 = 576
=> 48.(4 + 8 ) = 43 + 83
V )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
a, 1 x 2 x 3 x ... x 8 x 9 - 1 x 2 x 3 x ... x 8 - 1 x 2 x 3 x ... x 7 x 8 x 8
= 1 x 2 x 3 x ... x 8 ( 9 - 1 - 8 ) = 1 x2 x 3 x ... x 8 . 0 = 0
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