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1, \(\frac{1}{2}-\left(6\frac{5}{9}+x-\frac{117}{8}\right):\left(12\frac{1}{9}\right)=0\)
\(\left(\frac{6.9+5}{9}+x-\frac{117}{8}\right):\frac{12.9+1}{9}=\frac{1}{2}\)
( . là nhân nha)
\(\left(\frac{59}{9}-\frac{117}{8}+x\right):\frac{109}{9}=\frac{1}{2}\)
\(\frac{59}{9}-\frac{117}{8}+x=\frac{1}{2}\cdot\frac{109}{9}\)
\(\frac{59}{9}-\frac{117}{8}+x=\frac{109}{18}\)
\(x=\frac{109}{18}-\frac{59}{9}+\frac{117}{8}\)
\(x=\frac{113}{8}\)
( \(\left(y+\frac{1}{3}\right)+\left(y+\frac{2}{9}\right)+\left(y+\frac{1}{27}\right)+\left(y+\frac{1}{81}\right)=\frac{56}{81}\)
\(y+\frac{1}{3}+y+\frac{2}{9}+y+\frac{1}{27}+y+\frac{1}{81}=\frac{56}{81}\)
\(4y+\frac{1}{3}+\frac{2}{9}+\frac{1}{27}+\frac{1}{81}=\frac{56}{81}\)
\(4y+\frac{49}{81}=\frac{56}{81}\)
\(4y=\frac{7}{81}\)
y = 7/81:4
y = 7/324
\(\left(a\right)\frac{34-x}{30}=\frac{5}{6}\)
\(\frac{34-x}{30}=\frac{25}{30}\)
34 - x = 25
x = 34 - 25 = 9
\(\left(b\right)\frac{x+13}{34}=\frac{12}{17}\)
\(\frac{x+13}{34}=\frac{24}{34}\)
x + 13 = 24
x = 24 - 13 = 11
\(\left(c\right)\left(x+\frac{1}{3}\right)+\left(x+\frac{1}{9}\right)+\left(x+\frac{1}{27}\right)+\left(x+\frac{1}{81}\right)=\frac{56}{81}\)
\(4x+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}=\frac{56}{81}\)
Đặt \(A=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\)
Ta có : \(3A=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}\)
\(3A-A=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}-\frac{1}{3}-\frac{1}{9}-\frac{1}{27}-\frac{1}{81}\)
\(2A=1-\frac{1}{81}=\frac{80}{81}\)
\(A=\frac{80}{81}\div2=\frac{40}{81}\)
\(\Rightarrow4x+\frac{40}{81}=\frac{56}{81}\)
\(4x=\frac{56}{81}-\frac{40}{81}\)
\(4x=\frac{16}{81}\)
\(x=\frac{16}{81}\div4=\frac{4}{81}\)
a, Gọi biểu thức đó là A
Ta có :
A = \(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)
A x 3 = \(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}-\frac{1}{729}\)
A x 3 = \(1+A-\frac{1}{729}\)
A x 3 = \(\frac{728}{729}+A\)
A x 2 + A = \(\frac{728}{729}+A\)
A x 2 = \(\frac{728}{729}\)(bỏ A ở cả 2 vế)
A = \(\frac{728}{729}\div2=\frac{364}{729}\)
Đáp án = \(\frac{364}{729}\)
b, Phần này mình nghĩ là bạn sai đề rồi. Phải là \(\frac{45\times16-17}{45\times15+28}\)
Đặt A = \(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)
3A = \(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)
3A - A = (\(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)) - (\(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\))
2A = 1 - \(\frac{1}{729}\) = \(\frac{728}{729}\)
A = \(\frac{728}{729}:2=\frac{364}{729}\)
Đặt \(A=\frac{1}{3}+\frac{1}{9}+.......+\frac{1}{59049}\)
\(3A=3.\left(\frac{1}{3}+\frac{1}{9}+......+\frac{1}{59049}\right)\)
\(3A=1+\frac{1}{3}+........+\frac{1}{19683}\)
\(3A-A=\left(1+\frac{1}{3}+......+\frac{1}{19683}\right)-\left(\frac{1}{3}+\frac{1}{9}+........+\frac{1}{59049}\right)\)
\(2A=1-\frac{1}{59049}\)
\(2A=\frac{59048}{59049}\)
\(A=\frac{59048}{59049}:2\)
\(A=\frac{59048}{118098}\)
\(\text{Đặt : }A=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)
\(\Rightarrow3A=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)
\(\Rightarrow3A-A=1-\frac{1}{729}\)
\(\Rightarrow2A=\frac{728}{729}\)
\(\Rightarrow A=\frac{728}{729}:2=\frac{364}{729}\)
Đặt \(D=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}+\frac{1}{2187}\)
\(\Leftrightarrow D=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+\frac{1}{3^5}+\frac{1}{3^6}+\frac{1}{3^7}\)
\(\Leftrightarrow3D=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+\frac{1}{3^5}+\frac{1}{3^6}\)
\(\Leftrightarrow3D-D=2D=1-\frac{1}{3^6}\)
\(\Leftrightarrow D=\left(1-\frac{1}{3^6}\right)\div2\)
b)4y+(1/3+1/9+1/27)=56/81
4y+40/81=56/81
4y=56/81-40/81
4y=16/81
y=16/81:4
y=4/81
b) Tìm y:
( y + \(\frac{1}{3}\)) + ( y + \(\frac{1}{9}\)) + ( y + \(\frac{1}{27}\)) + ( y + \(\frac{1}{81}\)) = \(\frac{56}{81}\)
y + ( \(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\)) = \(\frac{56}{81}\)
y + \(\frac{27+9+3+1}{81}\) = \(\frac{56}{81}\)
y + \(\frac{40}{81}\) = \(\frac{56}{81}\)
y = \(\frac{56}{81}-\frac{40}{81}\)
y = \(\frac{16}{81}\)
Tl roy, ủng hộ nha! :)