6 = 2.3

Vì a + b + c \(⋮\)27

=> a + b + c \(⋮\)3

mà abc \(⋮\)2 

=> abc \(⋮\)6 

Study well 

Vì a + b + c \(⋮\)27

\(\Rightarrow\)abc \(⋮\)27

\(\Rightarrow\)abc \(⋮\)3³

\(\Rightarrow\)abc\(⋮\)3

Lại có : abc \(⋮\)2

mà ƯCLN(2;3) = 1

\(\Rightarrow\)abc\(⋮\)2.3

\(\Rightarrow\)abc\(⋮\)6 (đpcm)

\(\left(15,3-x\right)^8=\left(x-15,3\right)^7\)

\(\Rightarrow\left(x-15,3\right)^8=\left(x-15,3\right)^7\)

\(\Rightarrow\left(x-15,3\right)^8-\left(x-15,3\right)^7=0\)

\(\Rightarrow\left(x-15,3\right)^7\left(x-15,3-1\right)=0\)

\(\Rightarrow\left(x-15,3\right)\left(x-16,3\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x-15,3=0\\x-16,3=0\end{cases}\Rightarrow\orbr{\begin{cases}x=15,3\\x=16,3\end{cases}}}\)

Vậy \(x\in\left\{15,3;16,3\right\}\)

O x y z m n

a) Do Oy nằm giữa Ox và Oz (vì \(\widehat{xOy}< \widehat{xOz}\)) nên \(\widehat{xOy}+\widehat{yOz}=\widehat{xOz}\)

=> \(\widehat{yOz}=\widehat{xOz}-\widehat{xOy}=120^0-40^0=80^0\)

b) Do Om là tia p/giác của \(\widehat{xOy}\)nên :

 \(\widehat{xOm}=\widehat{mOy}=\frac{\widehat{xOy}}{2}=40^0=20^0\)

Do On là tia p/giác của \(\widehat{xOz}\)nên :

 \(\widehat{xOn}=\widehat{nOz}=\frac{\widehat{xOz}}{2}=\frac{120^0}{2}=60^0\)

Do Om nằm giữa Ox và On (\(\widehat{xOm}< \widehat{xOn}\)) nên \(\widehat{xOm}+\widehat{mOn}=\widehat{xOn}\)

=> \(\widehat{mOn}=\widehat{xOn}-\widehat{xOm}=60^0-20^0=40^0\)

c) Do Oy nằm giữa Om và On (Vì \(\widehat{nOy}< \widehat{nOm}\)) nên \(\widehat{nOy}+\widehat{yOm}=\widehat{nOm}\)

=> \(\widehat{nOy}=\widehat{mOn}-\widehat{mOy}=40^0-20^0=20^0\)

=> \(\widehat{nOy}=\widehat{yOm}=\frac{\widehat{mOn}}{2}=20^0\)

=> Oy là tia p/giác của góc mOn

\(\left(1-2x\right)^3=-125\Rightarrow1-2x=-5.\)

\(\Rightarrow-2x=-6\Leftrightarrow x=3\)

ĐỀ SAI THÌ PHẢI BẠN Ạ

     \(\left(15x-3\right)^{2019}=1=1^{2019}\)

\(\Rightarrow15x-3=1\)

\(\Rightarrow15x=3\)

\(\Rightarrow x=\frac{3}{15}\)

\(\Rightarrow x=\frac{1}{5}\)

=>(15x-3)²⁰¹⁹=1²⁰¹⁹

^=>15X-3=1

^=>15X=4

^=>X=4/15

 ^{GIÚP MK LÊN 333 SP NHÉ}

264 chia cho a dư 24 => 264 - 24 chia hết cho a => 240 chia hết cho a => a Ư( 240 )

363 chia cho a dư 43 => 363 - 43 chia hết cho a => 320 chia hết cho a => a Ư( 320 )

 => ƯCLN( 240; 320 ) = 80

Vậy a = 80

Vì a: 264( dư 24)

   a: 363( dư 43)

=> a+20 thì chia hết cho 264, a chia hết cho 363

=> a+20\(\in\)Ư{264;363}

264= 2³.3.11

363=3.131

a+20\(\in\)Ư{264;363}=Ư{3}={1;3}

=> a=Ư{-19; -17}

Vậy a=-19

      a=-17

Mk k chắc đâu nhé, mk chỉ làm thế chứ k tính kĩ đâu!

\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+..+\frac{1}{x\left(x+2\right)}=\frac{20}{41}\)

\(\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{x.\left(x+2\right)}\right)=\frac{20}{41}\)

\(\frac{1}{2}\left(\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{\left(x+2\right)-x}{x\left(x+2\right)}\right)=\frac{20}{41}\)

\(\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{20}{41}\)

\(\frac{1}{2}\left(1-\frac{1}{x+2}\right)=\frac{20}{41}\)

\(1-\frac{1}{x+2}=\frac{20}{41}:\frac{1}{2}\)

\(1-\frac{1}{x+2}=\frac{40}{41}\)

\(\frac{1}{x+2}=1-\frac{40}{41}\)

\(\frac{1}{x+2}=\frac{1}{41}\)

\(x+2=41\)

\(x=41-2\)

\(x=39\)

Tìm x 

a) \(\frac{1}{1\times3}+\frac{1}{3\times5}+\frac{1}{5\times7}+...+\frac{1}{x\times\left(x+2\right)}=\frac{20}{41}\)

\(\Rightarrow\frac{1}{2}\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{x\times\left(x+1\right)}\right)=\frac{20}{41}\)

\(\Rightarrow\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{x\times\left(x+2\right)}=\frac{20}{41}:\frac{1}{2}\)

\(\Rightarrow\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{x\times\left(x+2\right)}=\frac{40}{41}\)

\(\Rightarrow1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{\left(x+2\right)}=\frac{40}{41}\)

\(\Rightarrow1-\frac{1}{x+2}=\frac{40}{41}\)

\(\Rightarrow\frac{1}{x+2}=1-\frac{40}{41}\)

\(\Rightarrow\frac{1}{x+2}=\frac{1}{41}\)

\(\Rightarrow x+2=41\)

\(\Rightarrow x=41-2\)

\(\Rightarrow x=39\)

Vậy x = 39

a) Ta có : 4.5.6.7 + 8.9.10

             = 4.5.6.7 + 8.9.5.2

             = 5.(4.6.7 + 8.9.2) \(⋮\)5

=> 4.5.6.7 + 8.9.10   \(⋮\)5

=> 4.5.6.7 + 8.9.10  là hợp số

b) Ta có : 3.5.7.9 + 11.13.17.19

            = ...5 + ....1

            = ...6 \(⋮\)2

=> 3.5.7.9 + 11.13.17.19 \(⋮\)2

=> 3.5.7.9 + 11.13.17.19 là hợp số 

c) Ta có : 2341 + 4564 

          = 6905 \(⋮\)5

=> 2341 + 4564 \(⋮\)5

=> 2341 + 4564  là hợp số

d) Ta có : 7.9.11 - 3.5.7

 => 7.9.11 - 3.5.7 \(⋮\)7

=> 7.9.11 - 3.5.7 là hợp số