\(\left(x+5\right)+\left(x+10\right)+...+\left(x+25\right)-125=150\)
\(\Leftrightarrow x+5+x+10+...+x+25-125=150\)
\(\Leftrightarrow5x-50=150\)
\(\Leftrightarrow5x=100\)
\(\Leftrightarrow x=\dfrac{100}{5}=20\)
Vậy \(x=20\)

x = 20

CÓ CÁI NỊT

\(A=1+3+3^2+...+3^{2002}\)

\(3A=3+3^2+3^3+...+3^{2003}\)

\(2A=3A-A=3^{2003}-1\Rightarrow A=\dfrac{3^{2003}-1}{2}\)

A = \(\dfrac{3^{2003}-1}{2}\)

\(\dfrac{7^{45}}{7}=7^{44}\)

\(49.7^{20}=7^2.7^{20}=7^{22}\)

\(\Rightarrow\dfrac{7^{45}}{7}=7^{44}>7^{22}=49.7^{20}\)

7⁴⁵ : 7 ²³ =  7²² 

49 \(\times\) 7²⁰ = 7² \(\times\) 7²⁰ = 7²²

7⁴⁵ : 7²³ = 49 \(\times\) 7²⁰

\(S=1+2+2^2+2^3+...+2^9\)

\(\Rightarrow S=\dfrac{2^{9+1}-1}{2-1}\)

\(\Rightarrow S=2^{10}-1\)

\(\Rightarrow S=2^2.2^8-1\)

\(\Rightarrow S=4.2^8-1< 5.2^8\)

Vậy \(S< 5.2^8\)

So sánh S với \(5.2^8\)

24 = 2³.3

10 = 2.5

ƯCLN(24,10) = 2

BCNN(24; 10) =  2³.3.5 = 120

\(2014.2013.2013.2012.x=2011.2012.2013.2014\)

\(\Rightarrow x=\dfrac{2011.2012.2013.2014}{2014.2013.2013.2012}\)

\(\Rightarrow x=\dfrac{2011}{2013}\)

Bạn xem lại đề

1/

Số cần tìm \(\overline{ab7}\) theo đề bài

\(\overline{7ab}=2.\overline{ab7}+21\)

\(\Rightarrow700+\overline{ab}=20.\overline{ab}+14+21\)

\(\Leftrightarrow19.\overline{ab}=665\Rightarrow\overline{ab}=665:19=35\)

Số cần tìm là 357

2/

Gọi số cần tìm là \(\overline{ab}\) theo đề bài

\(\overline{ba}-\overline{ab}=63\)

\(10.b+a-10.a-b=63\)

\(9.\left(b-a\right)=63\Rightarrow b-a=7\)

\(a=\left(9-7\right):2=1\)

\(\Rightarrow b=9-a=9-1=8\)

Số cần tìm là 18