\(\dfrac{2}{5}:\dfrac{6}{25}\\ =\dfrac{2}{5}\times\dfrac{25}{6}\\ =\dfrac{2}{5}\times\dfrac{5\times5}{2\times3}=\dfrac{5}{3}\)

\(\dfrac{2}{5}:\dfrac{6}{25}\)

\(=\dfrac{2}{5}\times\dfrac{25}{6}\)

\(=\dfrac{2}{5}\times\dfrac{5\times5}{2\times3}\)

\(=\dfrac{5}{3}\)

\(D=4^2+4^3+...+4^{25}\)

\(\Rightarrow4D=4^3+4^4+...+4^{26}\)

\(\Rightarrow3D=4D-D=4^3+4^4+...+4^{26}-4^2-4^3-...-4^{25}=4^{26}-4^2\)

\(\Rightarrow D=\dfrac{4^{26}-4^2}{3}\)

kết quả:

\(\Rightarrow\left[{}\begin{matrix}2x-3=5\\2x-3=-5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4\\x=-1\end{matrix}\right.\)

50976:25=2039(dư 1)

2039 ( dư 1 )

\(\frac{a+b+c}{2}=\frac{a+b-7}{4c}=\frac{b+c+3}{4a}=\frac{a+c+4}{4b}.\)

TH1: \(a+b+c=0\)

=> \(\hept{\begin{cases}a+b-7=0\\b+c+3=0\\a+c+4=0\end{cases}}\)

=> a + b - 7 + b + c + 3 - a - c - 4 =0 

=> 2b -8 =0

=>  2b = 4 

=> b = 2.

=> a = 5; c = - 5

=> A = 20a + 11b + 2017c = 20.5 + 11.2 + 2017 ( -5) = -9963.

TH2: a + b + c khác 0.

Áp dụng dãy tỉ số bằng nhau:

\(\frac{a+b+c}{2}=\frac{a+b-7}{4c}=\frac{b+c+3}{4a}=\frac{a+c+4}{4b}\)

\(=\frac{a+b-7+b+c+3+a+c+4}{4c+4a+4b}=\frac{2a+2b+2c}{4a+4b+4c}=\frac{1}{2}\)(1)

=> \(\hept{\begin{cases}a+b-7=2c\\b+c+3=2a\\a+c+4=2b\end{cases}\Rightarrow}\hept{\begin{cases}a+b=2c+7\left(1\right)\\b+c=2a-3\left(2\right)\\a+c=2b-4\left(3\right)\end{cases}}\)

Từ (1) => \(a+b+c=1\left(4\right)\)

Từ (1); (4) => 2c + 7 + c = 1 => 3c = -6 => c = -2

Từ (2); (4) => 2a - 3 + a = 1 => 3a = 4  => a = 4/3

Từ (3); (4) => 2b - 4 + b = 1 => 3b = 5 => b = 5/3

=>  A = 20a + 11b + 2017c = \(20.\frac{4}{3}+11.\frac{5}{3}+2017.\left(-2\right)=-3989\)

\(3x^2-3+2x^4+6x^2-4-5x-8x^3=2x^4-8x^3-3x^2-5x-7\)