a: \(\Leftrightarrow\dfrac{32}{x}=\dfrac{2}{15}+\dfrac{2}{35}+...+\dfrac{2}{99}\)

=>32/x=1/3-1/5+1/5-1/7+...+1/9-1/11

=>32/x=1/3-1/11=8/33

=>x=32:8/33=132

b: \(\Leftrightarrow1-\dfrac{1}{6}+1-\dfrac{1}{12}+...+1-\dfrac{1}{56}=\dfrac{x}{16}\)
\(\Leftrightarrow6-\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{7}-\dfrac{1}{8}\right)=\dfrac{x}{16}\)

=>x/16=6-1/2+1/8=11/2+1/8=45/8=90/16

=>x=90

c: \(\Leftrightarrow\dfrac{22}{x}=\left(1-\dfrac{1}{2}\right)\left(1+\dfrac{1}{2}\right)\cdot\left(1-\dfrac{1}{3}\right)\left(1+\dfrac{1}{3}\right)\cdot...\cdot\left(1-\dfrac{1}{10}\right)\left(1+\dfrac{1}{10}\right)\)

=>22/x=1/2*2/3*...*9/10*3/2*4/3*...*11/10

=>22/x=1/10*11/2=11/20=22/40

=>x=40

a) \(5x-65=5.3^2 \\ 5x-65=45\\5x=45+65\\5x=110\\x=22\)

b) \(200-(2x+6)=4^3\\2x+6=200-4^3\\2x+6=136\\2x=130\\x=65\)

c) \(2(x-51)=2.2^3+20\\2(x-51)=16+20\\2(x-51)=36\\x-51=18\\x=51+18=69\)

d) \(135-5(x+4)=35\\5(x+4)=135-45\\5(x-4)=90\\x-4=18\\x=18+4=22\)

e) \((2x-4)(15-3x)=0\\2(x-2).3(5-x)=0\\(x-2)(5-x)=0\\ \left[ \begin{array}{l}x-2=0\\5-x=0\end{array} \right. \\ \left[ \begin{array}{l}x=2\\x=5\end{array} \right.\)

f) \(2^{x+1} . 2^{2014}=2^{2016} \\ (2^{x+1} . 2^{2014}):2^{2014}=2^{2016} :2^{2014} \\ 2^{x=1}=2^{2016-2014} \\2^{x+1}=2^2\\x+1=2\\x=1\)

g) \(15+(x-1)^3=43\\(x-1)^3=15-42\\(x-1)^3=-27\\(x-1)^3=(-3)^3\\x-1=-3\\x=-2\)

h) \(15-x=17+(-9)\\15-x=17-9\\15-x=8\\x=15-8\\x=7\)

i) \(|x-5|=|-7|+|-4|\\|x-5|=7+4\\|x-5|=11\\ \left[ \begin{array}{l}x-5=11\\x-5=-11\end{array} \right. \\ \left[ \begin{array}{l}x=16\\x=-6\end{array} \right.\)

k) \(|x-3|-12=-9+|-7|\\|x-3|-12=-9+7\\|x-3|-12=-2\\|x-3|=10 \\ \left[ \begin{array}{l}x-3=10\\x-3=-10\end{array} \right. \\ \left[ \begin{array}{l}x=13\\x=-7\end{array} \right.\)

A.35 x 34 + 35 x 38 + 65 x 75 + 65 x 45

Câu này không tính hợp lí được

B. 12x 53 + 53 x 172 - 53 x 84

= 53 x (12 + 172 - 84)

= 53 x 100

= 5300

C. 36 x 28 + 36 x 82 + 64 x 69 + 64 x 41

= 36 x (28+82) + 64 x (69+41)

= 36 x 110 + 64 x 110

= (36+64) x 110

= 100 x 110

= 11 000

D. A = 1+2+3+...+100

= (1+ 100) x 50

= 101 x 50

= 5050

E. B =17+19+...+101+103

= (103 +17) x [(103 - 17):2 + 1]

= 120 x 44

=5280

G. D= 3x (12+13+14+15) + 3x(8+7+6+5)

= 3 x (5+6+7+8+12+13+14+15)

= 3 x (20 x 4)

= 3 x 80

=240

a) 10320

b) 5300

c) 11000

d) 5050

e) 2460

g)  240

Bài 1.

a, (x-2)-15=65

x-2=65+15

x-2=80

x=80+2

x=2

b, 115-2\(\times\)(x-3)=35

2\(\times\)(x-3)=115-35

2\(\times\)(x-3)=70

x-3=70:2

x-3=35

x=35+5

x=38

c, 35+2\(\times\)(x-3)=65

2\(\times\)(x-3)=65-35

2\(\times\)(x-3)=30

x-3=30:2

x-3=15

x=15+3

x=18

3\(\times\)(x-5)-16=11

3\(\times\)(x-5)=11+16

3\(\times\)(x-5)=27

x-5=27:3

x-5=9

x=9+5

x=14

Bài 2:

a, \(2^x-1=31\)

\(2^x=31-1\)

\(2^x=30\)

\(\Rightarrow\)Không có x thoả mãn điều kiện \(2^x=30\)

b, \(x^3-1=26\)

\(x^3=26+1\)

\(x^3=27\)

\(\Rightarrow x=3\) vì \(3^3=27\)

c, \(6^x-1+1=37\)

\(6^x-1=37-1\)

\(6^x-1=36\)

\(6^x=36+1\)

\(6^x=37\)

\(\Rightarrow\) Không có x thoả mãn điều kiện \(6^x=37\)

d, (x+2)\(^3\)-15\(^0\)=215

\(\left(x+2\right)^3-1=215\)

\(\left(x+2\right)^3=215+1\)

\(\left(x+2\right)^3=216\)

\(\left(x+2\right)^3=6^3\)

\(x+2=6\)

\(x=6-2\)

\(x=4\)

e, \(2\times\left(x-9\right)^2=2\)

\(\left(x-9\right)^2=2:2\)

\(\left(x-9\right)^2=1\)

\(\Rightarrow x-9=1\) vì \(1^2=1\)

x=1+9

x=10

g, \(3\times\left(x-5\right)^3=51\)

\(\left(x-5\right)^3=51:3\)

\(\left(x-5\right)^3=17\)

\(\Rightarrow\) Không có x thoả mãn điều kiện \(\left(x-5\right)^3=17\)

Nếu đúng thì tick cho mk nhé

Bài 1:

a)\(\left(x-2\right)-15=65\)

\(x-2=65+15\)

\(x-2=80\)

\(x=80+2\)

\(x=82\)

b)\(115-2\left(x-3\right)=35\)

\(2\left(x-3\right)=115-35\)

\(2\left(x-3\right)=80\)

\(x-3=80:2\)

\(x-3=40\)

\(x=40+3\)

c) \(35+2\left(x-3\right)=65\)

\(2\left(x-3\right)=65-35=30\)

\(x-3=30:2=15\)

\(x=15+3=18\)

d) \(3\left(x-5\right)-16=11\)

\(3\left(x-5\right)=11+16=27\)

\(x-5=27:3=9\)

\(x=9+5=14\)

Bài 2:

a) \(2^x-1=31\)

\(2^x=31+1=32\)

Vì \(2^5=32\Rightarrow x=5\)

b) \(x^3-1=26\)

\(x^3=26+1=27\)

Vì \(3^3=27\Rightarrow x=3\)

c)\(6^{x-1}+1=37\)

\(6^{x-1}=37-1=36\)

Vì \(6^6=36\Rightarrow x-1=6\Rightarrow x=6+1=7\)

d)\(\left(x+2\right)^3-15^0=215\)

\(\left(x+2\right)^3-1=215\)

\(\left(x+2\right)^3=215+1=216\)

Vì \(6^3=216\Rightarrow x+2=6\Rightarrow x=6-2=4\)

e)\(2\left(x-9\right)^2=2\)

\(\left(x-9\right)^2=2:2=1\)

Vì \(1^2=1\Rightarrow x-9=1\Rightarrow x=1+9=10\)

g) \(3\left(x-5\right)^3=51\)

\(\left(x-5\right)^3=51:3=17\)

Bài 1:

a)

\(\left(x-2\right)-15=65\)

\(x-2\) \(=65+15\)

\(x-2\) \(=\) \(80\)

\(x\) \(=80+2\)

\(x\) \(=82\)

b)

\(115-2\cdot\left(x-3\right)=35\)

\(2\cdot\left(x-3\right)=115-35\)

\(2\cdot\left(x-3\right)=80\)

\(x-3=80:2\)

\(x-3=40\)

\(x\) \(=40+3\)

\(x\) \(=43\)

c)

\(35+2\cdot\left(x-3\right)=65\)

\(2\cdot\left(x-3\right)=65-35\)

\(2\cdot\left(x-3\right)=30\)

\(x-3=30:2\)

\(x-3=15\)

\(x\) \(=15+3\)

\(x\) \(=18\)

d)

\(3\cdot\left(x-5\right)-16=11\)

\(3\cdot\left(x-5\right)\) \(=11+16\)

\(3\cdot\left(x-5\right)\) \(=27\)

\(x-5\) \(=27:3\)

\(x-5\) \(=9\)

\(x\) \(=9+5\)

\(x\) \(=14\)

Bài 2

a)

\(2^x-1=31\)

\(2^x\) \(=31+1\)

\(2^x\) \(=32\)

\(2^x\) \(=2^5\)

⇒ \(x=5\)

b)

\(x^3-1=26\)

\(x^3\) \(=26+1\)

\(x^3\) \(=27\)

\(x^3\) \(=3^3\)

⇒ \(x=3\)

c)

\(6^{x-1}+1=37\)

\(6^{x-1}\) \(=37-1\)

\(6^{x-1}\) \(=36\)

\(6^{x-1}\) \(=6^2\)

➞ \(x-1=2\)

\(x\) \(=2+1\)

\(x\) \(=3\)

d)

\(\left(x+2\right)^3-15^0=215\)

\(\left(x+2\right)^3-1=215\)

\(\left(x+2\right)^3=215+1\)

\(\left(x+2\right)^3=216\)

\(\left(x+2\right)^3=6^3\)

➞ \(x+2=6\)

\(x=6-2\)

\(x=4\)

e)

\(2\cdot\left(x-9\right)^2=2\)

\(\left(x-9\right)^2=2:2\)

\(\left(x-9\right)^2=1\)

\(\left(x-9\right)^2=1^2\)

➞ \(x-9=1\)

\(x=9+1\)

\(x=10\)

g)

\(3\cdot\left(x-5\right)^3=51\)

Câu hỏi này sai nhé bạn

A=1/3*5 + 1/5*7 + ....+ 1/99*101

A=1/2(2/3*5 + 2/5*7 + ...+ 2/99*101)

A=1/2[(1/3-1/5)+(1/5-1/7)+...+(1/99-1/101)]

A=1/2(1/3-1/101)

A=1/2 * 98/303

A=49/303

\(A=\frac{1}{5}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+...+\frac{1}{9999}\)

\(=\frac{1}{3X5}+\frac{1}{5X7}+\frac{1}{7X9}+\frac{1}{9X11}+...+\frac{1}{99X101}\)

\(2A=\frac{2}{3X5}+\frac{2}{5X7}+\frac{2}{7X9}+\frac{2}{9X11}+...+\frac{2}{99X101}\)

\(=\frac{5-3}{3X5}+\frac{7-5}{7X9}+\frac{9-7}{9X7}+\frac{11-9}{9X11}+...+\frac{101-99}{101}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{99}-\frac{1}{101}\)

\(=\frac{1}{3}-\frac{1}{101}=\frac{98}{303}\)

Từ đó ta suy ra:\(A=\frac{98}{303}:2=\frac{49}{303}\)

tinh nhanh a= 1/15 + 1/35 + 1/65 + 1/99 ... + 1/9999

Bài 1:

a) \(24 - (-15) - 2\)

\(=39-2\)

\(=37\)

b) \((-85) + 10 - (-85) - 50\)

\(=[(-85)-(-85)]+10-50\)

\(=0+10-50\)

\(=10-50\)

\(=-40\)

c) \(71 - (-30) - (+18) + (-30)\)

\(=[(-30)-(-30)]+71-(+18)\)

\(=0+71-18\)

\(=71-18\)

\(=53\)

d) \(-(30) - (+37) + (+37) + (-85)\)

\(=[-(+37)+(+37)]-(30)+(-85)\)

\(=0-(30)+(-85)\)

\(=(-30)+(-85)\)

\(=-115\)

e) \((35-815) - (795-65)\)

\(=(-780)-730\)

\(=-1510\)

g) \((2002-79+15) + (-79+15)\)

\(=1938+(-64)\)

\(=1874\)

Bài 2:

a) \(25 - (30+x) = x - (27-8)\)

\(25-30-x=x-27+8\)

\(x+x=25-30+27-8\)

\(2x=14\)

\(x=14\div2\)

\(x=7\)

b) \((x-12) - 15 = (20-17) - (18+x) \)

\(x-12-15=13-18-x\)

\(x-27=-5-x\)

\(x+x=-5+27\)

\(2x=22\)

\(x=22\div2\)

\(x=11\)

c) \(15 - x = 7 - (-2)\)

\(15-x=9\)

\(x=15-9\)

\(x=6\)

d) \(x - 35 = (-12) - 3\)

\(x-35=-15\)

\(x=-15+35\)

\(x=20\)

e) \(\left|5-x\right|-26=-15\)

\(\left|5-x\right|=-15+26\)

\(\left|5-x\right|=11\)

Từ đây ta có:

*Nếu \(5-x=11\)

\(x=5-11\)

\(x=-6\)

*Nếu \(5-x=-11\)

\(x=5-(-11)\)

\(x=16\)

Vậy \(x=-6;x=16\)