x x5=1005-35
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\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+....+\frac{1}{x\times\left(x+2\right)}=\frac{1005}{2011}\)
\(\Leftrightarrow\frac{1}{2}\times\left(\frac{1}{1\times3}+\frac{1}{3\times5}+\frac{1}{5\times7}+.....+\frac{1}{x\times\left(x+2\right)}\right)=\frac{1005}{2011}\)
\(\Leftrightarrow\frac{1}{2}\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{1005}{2011}\)
\(\Leftrightarrow\frac{1}{2}\times\left(1-\frac{1}{x+2}\right)=\frac{1005}{2011}\)
\(\Leftrightarrow1-\frac{1}{x+2}=\frac{1005}{2011}:\frac{1}{2}=\frac{2010}{2011}\)
\(\Leftrightarrow\frac{1}{x+2}=1-\frac{2010}{2011}=\frac{1}{2011}\)
\(\Leftrightarrow x+2=2011\)
\(\Leftrightarrow x=2009\)
Vậy x = 2009
\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{x\left(x+2\right)}=\frac{1005}{2011}\)
\(\Rightarrow\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{x\left(x+2\right)}=\frac{1005}{2011}\)
\(\Rightarrow\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{1005}{2011}\)
\(\Rightarrow\frac{1}{2}\left(1-\frac{1}{x+2}\right)=\frac{1005}{2011}\)
\(\Rightarrow\frac{x+1}{x+2}=\frac{2010}{2011}\)
\(\Rightarrow x+1=2010\Leftrightarrow x=2009\)
\(\frac{\left(-5\right)^2.\left(-5\right)^3.16}{5^4.\left(-2\right)^4}=\frac{\left(-5\right)^5.16}{5^4.16}=\frac{\left(-5\right)^5}{5^4}=-5\)
\(\frac{14^{1005}.5^{1006}}{2^{1007}.35^{1004}}=\frac{14^{1005}.5^{1005}.5}{2^{1004}.2^3.35^{1004}}=\frac{\left(14.5\right)^{1005}.5}{\left(2.35\right)^{1004}.2^3}=\frac{70^{1005}.5}{70^{1004}.2^3}=\frac{70.5}{8}=\frac{350}{8}=\frac{175}{4}\)
Chúc bạn học tốt!
Toán lớp 6 ?
\(\frac{\left(-5\right)^2\left(-5\right)^3.16}{5^4.\left(-2\right)^4}=\frac{\left(-5\right)^5.2^4}{5^4.2^4}=-5\)
\(\frac{14^{1005}.5^{1006}}{2^{1007}.35^{1004}}=\frac{14^{1005}.5^{1005}.5}{2^{1004}.35^{1004}.2^3}=\frac{\left(14.5\right)^{1005}.5}{\left(2.35\right)^{1004}.8}=\frac{70^{1005}.5}{70^{1004}.8}=\frac{70.5}{8}=\frac{175}{4}\)
C = 48 x 12 + 48 x 3 + 35 x 5 + 13 x 5
C = 48 x (12 + 3) + 5 x (35 + 13)
C = 48 x 15 + 5 x 48
C = 48 x (15 + 5)
C = 48 x 20
C = 960
Đáp số là 960.
Tíck cho mìk vs nhé Kane !
C = 48 x 12 +48 x3 +35 x5 +13 x5
C = 48 x (12 + 3) + 5 x (35 + 13)
C = 48 x 15 + 5 x 48
C = 48 x (15 + 5)
C = 48 x 20
C = 960
\(\frac{14^{1005}.5^{1006}}{2^{1007}.35^{1004}}\)
\(=\frac{2^{1005}.7^{1005}.5^{1006}}{2^{1007}.5^{1004}.7^{1004}}\)
\(=\frac{5^2.7}{2^2}=\frac{25.7}{4}=\frac{175}{4}\)
TRẦN TIỂU HY ƠI, BẠN TRÌNH BÀY RA GIÙM MK NHA. MK KO HIỂU LẮM
(X - 1005) x (1 + 3 + 5+ 7 + 9 + 11) = 1989 x 1990 x (70 - 35 x 2)
(X - 1005) x (11 + 1)[(11 - 1) : 2 + 1): 2] = 1989 x 1990 x 0
(X - 1005) x 36 = 0
X - 1005 = 0 : 36
X - 1005 = 0
X = 1005
( x - 1005 ) . ( 1 + 3 + 5 + 7 + 9 + 11 ) = 1989 . 1990 . ( 70 - 35 . 2 )
( x - 1005 ) . 36 = 1989 . 1990 . ( 70 - 70 )
( x - 1005 ) . 36 = 1989 . 1990 . 0
( x - 1005 ) . 36 = 0
x - 1005 = 0
x = 1005
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Mình vừa làm cách đây 11 phút nhé !
Ta có : a2010 + b2010 + c2010 = a1005b1005 + b1005c1005 + c1005a1005
<=> 2a2010 + 2b2010 + 2c2010 = 2a1005b1005 + 2b1005c1005 + 2c1005a1005
<=> 2a2010 + 2b2010 + 2c2010 - 2a1005b1005 - 2b1005c1005 - 2c1005a1005 = 0
<=> (a2010 - 2a1005b1005 + b2010) + (b2010 - 2b1005c1005 + c2010) + (c2010 - 2c1005a1005 + a2010) = 0
<=> (a1005 - b1005)2 + (b1005 - c1005)2 + (c1005 - a1005 )2 = 0
=> a1005 - b1005 = b1005 - c1005 = c1005 - a1005 = 0
=> a = b = c
Vậy (a - b)20 + (b - c)11 + (c - a)2010 = (a - a)20 + (a - a)11 + (a - a)2010 = 0 + 0 + 0 = 0 .
135 - 3 ( x + 1 ) = 30
3 ( x + 1 ) = 105
x + 1 = 35
x = 34
\(1005^2\cdot1005^x=1005^7\)
\(1005^{2+x}=1005^7\)
=> x + 2 = 7
=> x = 5
Vậy,........
1005^2.1005^x=1005^7
<=>1005^2+x=1005^7
<=>2+x=7
<=>x=5
ai giúp mình vs
\(x\cdot5=1005-35\)
=>\(x\cdot5=970\)
=>\(x=\dfrac{970}{5}=194\)