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` 242/363 + 1616/2121 = 2/7 xxy`
`2/7 xxy= 2/3 + 16/21`
`2/7 xxy= 14/21 +16/21`
`2/7 xxy= 30/21`
`y=10/7 : 2/7`
`y=10/7 xx 7/2`
`y=70/14`
`y=5`
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` (y + 1/4) + (y + 1/16) + (y + 1/16) =2`
`(y+y+y)+(1/4 + 1/16+1/16)=2`
`3y + (4/16 +1/16 +1/16)=2`
`3y + 6/16=2`
`3y=2-6/16`
`3y= 32/16-6/16`
`3y= 26/16`
`y=26/16 : 3`
`y=26/48`
`y=13/24`
\(a,\dfrac{242}{363}+\dfrac{1616}{2121}=\dfrac{2}{7}\times y\)
\(\dfrac{2}{7}\times y=\dfrac{2\times121}{3\times121}+\dfrac{16\times101}{21\times101}\)
\(\dfrac{2}{7}\times y=\dfrac{2}{3}+\dfrac{16}{21}\)
\(\dfrac{2}{7}\times y=\dfrac{14}{21}+\dfrac{16}{21}\)
\(\dfrac{2}{7}\times y=\dfrac{30}{21}\)
\(\dfrac{2}{7}\times y=\dfrac{10}{7}\)
\(y=\dfrac{10}{7}:\dfrac{2}{7}\)
\(y=\dfrac{10}{7}\times\dfrac{7}{2}\)
\(y=5\)
\(---\)
\(b,\left(y+\dfrac{1}{4}\right)+\left(y+\dfrac{1}{16}\right)+\left(y+\dfrac{1}{16}\right)=2\)
\(\left(y+y+y\right)+\left(\dfrac{1}{4}+\dfrac{1}{16}+\dfrac{1}{16}\right)=2\)
\(3\times y+\left(\dfrac{4}{16}+\dfrac{2}{16}\right)=2\)
\(3\times y+\dfrac{6}{16}=2\)
\(3\times y+\dfrac{3}{8}=2\)
\(3\times y=2-\dfrac{3}{8}\)
\(3\times y=\dfrac{16}{8}-\dfrac{3}{8}\)
\(3\times y=\dfrac{13}{8}\)
\(y=\dfrac{13}{8}:3\)
\(y=\dfrac{13}{8}\times\dfrac{1}{3}\)
\(y=\dfrac{13}{24}\)
#\(Toru\)
1/3+1/15+1/35+1/63+1/99+1/143+1/195
=1/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11*13+1/13*15
suy ra 2(1/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11*13+1/13*15)
=2/1*3+2/3*5+2/5*7+2/7*9+2/9*11+2/11*13+2/13*15
=1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15
=1-1/15
=14/15
a=14/15 chia 2=7/15
\(\left(\dfrac{242}{363}+\dfrac{1616}{2121}\right)=\dfrac{2}{7}.x\)
\(\Leftrightarrow\dfrac{242}{363}\left(1+\dfrac{8}{7}\right)=\dfrac{2}{7}.x\)
\(\Leftrightarrow\dfrac{242}{363}.\dfrac{15}{7}=\dfrac{2}{7}.x\)
\(\Leftrightarrow\dfrac{10}{7}=\dfrac{2}{7}.x\)
\(\Leftrightarrow x=\dfrac{10}{7}:\dfrac{2}{7}\)
\(\Leftrightarrow x=\dfrac{10}{7}.\dfrac{7}{2}\)
\(\Leftrightarrow x=5\)
\(\dfrac{242}{363}+\dfrac{1616}{2121}=\dfrac{2}{7}y\)
\(\dfrac{2\cdot121}{3\cdot121}+\dfrac{16\cdot101}{21\cdot101}=\dfrac{2}{7}y\)
\(\dfrac{2}{7}y=\dfrac{2}{3}+\dfrac{16}{21}\)
\(\dfrac{2}{7}y=\dfrac{10}{7}\)
\(y=\dfrac{10}{7}\div\dfrac{2}{7}=5\)
a) \(\dfrac{6}{13}:\left(\dfrac{1}{2}-x\right)=\dfrac{15}{39}\)
\(\dfrac{1}{2}-x=\dfrac{6}{13}:\dfrac{15}{39}\)
\(\dfrac{1}{2}-x=\dfrac{6}{5}\)
\(x=\dfrac{1}{2}-\dfrac{6}{5}\)
\(x=-\dfrac{7}{10}\)
b) \(3\times\left(\dfrac{x}{4}+\dfrac{x}{28}+\dfrac{x}{70}+\dfrac{x}{130}\right)=\dfrac{60}{13}\)
\(3\times x\times\left(\dfrac{1}{4}+\dfrac{1}{28}+\dfrac{1}{70}+\dfrac{1}{130}\right)=\dfrac{60}{13}\)
\(x\times\left(\dfrac{3}{1\times4}+\dfrac{3}{4\times7}+\dfrac{3}{7\times10}+\dfrac{3}{7\times13}\right)=\dfrac{60}{13}\)
\(x\times\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}\right)=\dfrac{60}{13}\)
\(x\times\left(1-\dfrac{1}{13}\right)=\dfrac{60}{13}\)
\(x\times\dfrac{12}{13}=\dfrac{60}{13}\)
\(x=\dfrac{60}{13}:\dfrac{12}{13}\)
\(x=5\)
242/363 + 1616/ 2121= 5/7 x y
\(\frac{2}{3}+\frac{16}{21}=\frac{5}{7}\)x y
\(\frac{14}{21}\)+\(\frac{16}{21}\)= \(\frac{5}{7}\)x y
\(\frac{10}{7}\)=\(\frac{5}{7}\)x y
\(\frac{10}{7}\): \(\frac{5}{7}\)=y
\(\frac{10}{7}\)x \(\frac{7}{5}\)=y
2=y
vậy y=2
\(\frac{242}{363}+\frac{1616}{2121}=\frac{5}{7}\times y\)
\(\frac{121\times2}{121\times3}+\frac{101\times16}{101\times21}=\frac{5}{7}\times y\)
\(\frac{2}{3}+\frac{16}{21}=\frac{5}{7}\times y\)
\(\frac{10}{7}=\frac{5}{7}\times y\)
\(\Rightarrow y=\frac{10}{7}:\frac{5}{7}\)
\(y=2\)
