\(3^{2x}.27=3^{11}\)

 \(3^{2x}.3^3=3^{11}\)

 \(3^{2x+3}=3^{11}\)

\(2x+3=11\)

\(2x=11-3\)

\(2x=8\)

\(x=4\)

3^2x . 27 = 3¹¹

=> 3^2x.3³ = 3¹¹

=> 3^{2x + 3} = 3¹¹

=>  2x + 3 = 11

=>  2x       = 11 - 3

=> 2x        = 8

=>   x        = 8 : 2

=>   x        = 4

2³ . 5 - ( x + 3² ) = 10

8 . 5 - ( x + 9 ) = 10

 x + 9 = 40 - 10

 x + 9 = 30

  x = 21

Vậy x = 21

\(2^3.5-\left(x+3^2\right)=10\Leftrightarrow8.5-\left(x+3^2\right)=10\)

\(40-\left(x+3^2\right)=10\)

\(x+3^2=40-10\)

\(x+9=30\)

\(x=30-9=21\)

\(5\left(x+35\right)-2^3.5^2=2^5.3^2-3.31\)

\(5x+175-8.25=32.9-3.31\)

\(5x+175-200=288-93\)

\(5x-25=195\)

\(5x=195+25\)

\(5x=220\)

\(x=220:5\)

\(x=44\)

Để phân số này thuộc N nốt hả ?

Để biểu thức là STN

\(\Rightarrow n^2+3n⋮n-1\)

\(\Rightarrow n^2-n+4n⋮n-1\)

\(\Rightarrow n.\left(n-1\right)+4n⋮n-1\)

Mà  \(n.\left(n-1\right)⋮n-1\)

\(\Rightarrow4n⋮n-1\)

\(\Rightarrow4n-4+4⋮n-1\)

\(\Rightarrow4.\left(n-1\right)+4⋮n-1\)

Mà \(4.\left(n-1\right)⋮n-1\)

\(\Rightarrow4⋮n-1\)

\(\Rightarrow n-1\inƯ\left(4\right)=\left\{1;2;4\right\}\)

\(\Leftrightarrow n\in\left\{2;3;5\right\}\)

\(\frac{5}{17}\left(3\frac{1}{7}+8\frac{7}{3}\right)\frac{15}{17}\left(3\frac{7}{6}+8\frac{1}{7}\right)=\frac{5}{17}\left(\frac{22}{7}+\frac{31}{3}\right)\frac{15}{17}\left(\frac{25}{6}+\frac{57}{7}\right)\)

\(=\frac{5}{17}.\frac{283}{21}.\frac{15}{17}.\frac{517}{42}=\frac{10973325}{254898}=\frac{3657775}{84966}\)