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\(\left(x+1\right)\cdot\left(x+2\right)\cdot\left(x+3\right)\cdot...\cdot\left(x+20\right)=240\)
\(\left(x+x+x+...+x\right)\cdot\left(1+2+3+...+20\right)=240\)
\(20x\cdot210=240\)
\(20x=\frac{240}{210}=\frac{8}{7}\)
\(\Rightarrow x=\frac{8}{7}\div20=\frac{2}{35}\)
1) \(2^3\times x-5^2\times x=2\times\left(5^2+2^2\right)-33\)
\(x\times\left(2^3-5^2\right)=2\times\left(25+4\right)-33\)
\(x\times\left(8-25\right)=2\times29-33\)
\(x\times-17=25\)
\(x=-\dfrac{25}{17}\)
2) \(15\div\left(x+2\right)=\left(3^3+3\right)\div1\)
\(15\div\left(x+2\right)=\left(27+3\right)\div1\)
\(15\div\left(x+2\right)=30\div1\)
\(15\div\left(x+2\right)=30\)
\(x+2=\dfrac{1}{2}\)
\(x=-\dfrac{3}{2}\)
3) \(20\div\left(x+1\right)=\left(5^2+1\right)\div13\)
\(20\div\left(x+1\right)=\left(25+1\right)\div13\)
\(20\div\left(x+1\right)=26\div13\)
\(20\div\left(x+1\right)=2\)
\(x+1=20\div2\)
\(x+1=10\)
\(x=9\)
4) \(320\div\left(x-1\right)=\left(5^3-5^2\right)\div4+15\)
\(320\div\left(x-1\right)=\left(125-25\right)\div4+15\)
\(320\div\left(x-1\right)=100\div4+15\)
\(320\div\left(x-1\right)=25+15\)
\(320\div\left(x-1\right)=40\)
\(x-1=8\)
\(x=9\)
5) \(240\div\left(x-5\right)=2^2\times5^2-20\)
\(240\div\left(x-5\right)=4\times25-20\)
\(240\div\left(x-5\right)=100-20\)
\(240\div\left(x-5\right)=80\)
\(x-5=30\)
\(x=35\)
6) \(70\div\left(x-3\right)=\left(3^4-1\right)\div4-10\)
\(70\div\left(x-3\right)=\left(81-1\right)\div4-10\)
\(70\div\left(x-3\right)=80\div4-10\)
\(70\div\left(x-3\right)=20-10\)
\(70\div\left(x-3\right)=10\)
\(x-3=7\)
\(x=10\)
Ta có: ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + .... + ( x + 9 ) + ( x + 10 ) = 240
<=> ( x + x + x + ...+ x ) + ( 1 + 2 + 3 + ... +10 ) = 240
<=> 10x + 55 = 240
=> 55 + 10x = 240
=> 10x = 240 - 55
=> 10x = 185
=> x = 185 : 10 = 18,5
Vậy x = 18.5
(x +1) + (x + 2) + ( x + 3) + .....+ ( x + 9) +( x + 10) = 240
x * 10 + ( 1 + 2 +... + 10 ) = 240
x * 10 + \(\frac{10.11}{2}\)=240
x*10+55=240
x*10 = 240 - 55
x * 10 = 185
x = 185 : 10
x = 18,5
a, \(15:\left(x+2\right)=3\Leftrightarrow x+2=3\Leftrightarrow x=1\)
b, \(20:\left(x+1\right)=2\Leftrightarrow x+1=10\Leftrightarrow x=9\)
c, \(240:\left(x-5\right)=2^2.5^2-20=80\Leftrightarrow x-5=3\Leftrightarrow x=8\)
d, \(96-3\left(x+1\right)=42\Leftrightarrow3\left(x+1\right)=54\Leftrightarrow x+1=18\Leftrightarrow x=17\)
a) 15 : (x + 2) = 3
x + 2 = 15 : 3
x + 2 = 5
x = 5 – 2 = 3
b) 20 : (1 + x) = 2
1 + x = 20 : 2
1 + x = 10
x = 10 – 1 = 9
c) 240 : (x – 5) = 22.52 – 20
240 : (x – 5) = 4.25 – 20
240 : (x - 5) = 100 – 20
240 : (x - 5) = 80
x – 5 = 240 : 80
x – 5 = 3
x = 3 + 5 = 8
d) 96 - 3(x + 1) = 42
3(x + 1) = 96 – 42
3(x + 1) = 54
x + 1 = 54 : 3
x + 1 = 18
x = 18 – 1
x = 17
a) 2 + 4 + 6 + ... + x = 240
số số hạng : ( x - 2 ) : 2 + 1 = x : 2 ( số )
tổng : ( x + 2 ) . x : 2 = 240
( x + 2 ) . x = 240 x 2
( x + 2 ) . x = 480
Mà .... ( đề sai )
b) 1 + 2 + 3 + ... + x = 306
số số hạng : ( x - 1 ) : 1 + 1 = x ( số )
tổng : ( x + 1 ) . x : 2 = 306
( x + 1 ) . x = 306 . 2
( x + 1 ) . x = 612
Mà .... ( đề sai )
a ) \(15:\left(x+2\right)=3\)
\(\left(x+2\right)=15:3\)
\(x+2=5\)
\(x=5-2\)
\(x=3\)
Vậy \(x=3\)
b) \(20:\left(1+x\right)=2\)
\(\left(1+x\right)=20:2\)
\(1+x=10\)
\(x=10-1\)
\(x=9\)
Vậy \(x=9\)
c) \(240:\left(x-5\right)=2^2.5^2=20\)
\(240:\left(x-5\right)=4.25=20\)
\(240:\left(x-5\right)=100=20\)
\(\Rightarrow\orbr{\begin{cases}240:\left(x-5\right)=100\\240:\left(x-5\right)=20\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}\left(x-5\right)=240:100\\\left(x-5\right)=240:20\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x-5=2,4\\x-5=12\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=2,4+5\\x=12+5\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=7,4\\x=17\end{cases}}\)
Vậy \(x=7,4\)hoặc \(x=17\)
d) \(96-3\left(x+1\right)=12\)
\(3\left(x+1\right)=96-12\)
\(3\left(x+1\right)=84\)
\(\left(x+1\right)=84:3\)
\(x+1=28\)
\(x=28-1\)
\(x=27\)
Vậy \(x=27\)
Chúc bạn học tốt !!!
Số số hạng của dãy số trên là:
(x-1):1+1=x (số hạng)
=> 1+2+3+4+...+x=\(\frac{\left(x+1\right)x}{2}=240\)
=> (x+1)x=480
#Bạn check lại đề nha, đề sai hay sao ý, mình làm đến đây ko tách được ra 2 số tự nhiên liên tiếp cho tích bằng 480 được nữa ạ. Hay là mình bị lag nhờ '-'??
\(\left(x\times1\right)+\left(x\times2\right)+\left(x\times3\right)+....+\left(x\times10\right)=240\)
\(\left(x\times x\times x\times....\times x\right)\times\left(1+2+3+...+10\right)=240\)
\(1x\times\frac{\left(10+1\right).10}{2}=240\)
\(1x\times55=240\)
\(1x=240\div55\)
\(1x=\frac{48}{11}\)
\(\Rightarrow x=\frac{48}{11}\)