4 x y + (1/3 + 1/9 + 1/27 + 1/81) = 56/81

4 x y + (27/81 + 9/81 + 3/81 + 1/81) = 56/81

4 x y + 40/81 = 56/81

4 x y  = 56/81 - 40/81 = 16/81

y = 4/81

\(\left(y+\frac{1}{3}\right) +\left(y+\frac{1}{9}\right)+ \left(y+\frac{1}{27}\right)+\left(y+\frac{1}{81}\right)=\frac{56}{81}\)

\(y\cdot4+\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\right)=\frac{56}{81}\)

\(y\cdot4+\frac{40}{81}=\frac{56}{81}\)

\(y\cdot4=\frac{56}{81}-\frac{40}{81}\)

\(y\cdot4=\frac{16}{81}\)

     \(y=\frac{16}{81}:4\)

      \(y=\frac{4}{81}\)

(y+1/3)+(y+1/9)+(y+1/27)+(y+1/81)=56/81

=> y+1/3+y+1/9+y+1/27+y+1/81=56/81

=>4y+ 27/81+9/81+3/81+1/81=56/81

=> 4y+40/81=56/81

=>4y=16/81

=>y=4/81

1+3+9+27+......+y=1093
3x(1+3+9+27+.....+y)=1093x3
3+9+27+81+.....+3y=1093x3
=> 1093x3-1093= (3+9+27+.....3y)-(1+3+9+27+....+y)
<=> 1093x2=3y-1
<=>2186+1=3y
<=> 2187=3y
=> y=2187:3
y=729

\(\left(y+\frac{1}{3}\right)+\left(y+\frac{1}{9}\right)+\left(y+\frac{1}{27}\right)+\left(y+\frac{1}{81}\right)=\frac{56}{81}\)

\(\Leftrightarrow4y+\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\right)=\frac{56}{81}\)

\(\Leftrightarrow4y+\frac{40}{81}=\frac{56}{81}\)

\(\Leftrightarrow4y=\frac{56}{81}-\frac{40}{81}\)

\(\Leftrightarrow4y=\frac{16}{81}\)

\(\Rightarrow y=\frac{16}{81}\div4\)

\(\Rightarrow y=\frac{4}{81}\)

Vậy y có giá trị =\(\frac{4}{81}\)

< y   1/3 >    < y   1/9>  < y   1/27 >   < y   1/81 > =  56 / 81   

= 4y + < 1/3 + 1/9 + 1/27 + 1/81 >  = 56 / 81

= 4y + 40 / 81 = 56 / 81 

= 4y = 56 / 81 - 40 / 81

= 4 / 81

Lời giải:

a) 

$3^{2x+1}.7^y=9.21^x=3^2.(3.7)^x=3^{2+x}.7^x$

Vì $x,y$ là số tự nhiên nên suy ra $2x+1=2+x$ và $y=x$

$\Rightarrow x=y=1$

b) \(\frac{27^x}{3^{2x-y}}=\frac{3^{3x}}{3^{2x-y}}=3^{x+y}=243=3^5\Rightarrow x+y=5(1)\)

\(\frac{25^x}{5^{x+y}}=\frac{5^{2x}}{5^{x+y}}=5^{x-y}=125=5^3\Rightarrow x-y=3\) $(2)$

Từ $(1);(2)\Rightarrow x=4; y=1$

bài 1

A)37/60

B)13/45

C)1/4

bài 2

a)42/25:y/5=5/6

y=10,08

b)27/y:9/4=3/7

y=28

Tìm y :

( y + 1/3 ) + ( y + 1/9 ) + ( y + 1/27 ) + ( y + 1/81 ) = 56/81

 y + 1/3 + y + 1/9 + y + 1/27 + y  + 1/81 = 56/81

 y x 4 + ( 1/3 + 1/9 + 1/27 +1/81 ) = 56/81

 y x 4 + ( 27/81 + 9/81 + 3/81 + 1/81 ) = 56/81

 y x 4 + 40/81 = 56/81

 y x 4              = 56/81 - 40/81

 y x 4              = 16/81

 y                    = 16/81 : 4

 y                    = 4/81

thanks Vũ Thị Huyền nha

cái gì?