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nhân A với 5
nhân B với 2
Tỉ số là 5/2 bạn tự giải đầy đủ nhé mình ko bít viết kí hiệu PS
Chúc bạn học tốt!!
\(A=\frac{4}{7.31}+\frac{6}{7.41}+\frac{9}{10.41}+\frac{7}{10.57}\)
\(=\frac{20}{35.31}+\frac{30}{35.41}+\frac{45}{50.41}+\frac{35}{50.57}\)
\(=5\left(\frac{4}{35.31}+\frac{6}{35.41}+\frac{9}{50.41}+\frac{7}{50.57}\right)\)
\(=5\left(\frac{1}{31}-\frac{1}{35}+\frac{1}{35}-\frac{1}{41}+\frac{1}{41}-\frac{1}{50}+\frac{1}{50}-\frac{1}{57}\right)\)
\(=5\left(\frac{1}{31}-\frac{1}{57}\right)\)
\(B=\frac{7}{19.31}+\frac{5}{19.43}+\frac{3}{23.43}+\frac{11}{23.57}\)
\(=\frac{14}{34.31}+\frac{10}{38.43}+\frac{6}{46.43}+\frac{22}{46.57}\)
\(=2\left(\frac{7}{34.31}+\frac{5}{38.43}+\frac{3}{46.43}+\frac{11}{46.57}\right)\)
\(=2\left(\frac{1}{31}-\frac{1}{34}+\frac{1}{34}-\frac{1}{43}+\frac{1}{43}-\frac{1}{46}+\frac{1}{46}-\frac{1}{57}\right)\)
\(=2\left(\frac{1}{31}-\frac{1}{57}\right)\)
\(\Rightarrow\frac{A}{B}=\frac{5\left(\frac{1}{31}-\frac{1}{57}\right)}{2\left(\frac{1}{31}-\frac{1}{57}\right)}=\frac{5}{2}\)
Ta có:
\(\frac{A}{5}=\frac{4}{35\cdot31}+\frac{6}{35\cdot41}+\frac{9}{50\cdot41}+\frac{7}{50\cdot57}=\frac{35-31}{35\cdot31}+\frac{41-35}{35\cdot41}+\frac{50-41}{50\cdot41}+\frac{57-50}{50\cdot57}\) ( Ps cuối là\(\frac{57-50}{50.57}\) nha).
\(=\frac{1}{31}-\frac{1}{35}+\frac{1}{35}-\frac{1}{41}+\frac{1}{41}-\frac{1}{50}+\frac{1}{50}-\frac{1}{57}\)
\(\Rightarrow\frac{A}{5}=5\cdot\left(\frac{1}{31}-\frac{1}{57}\right)\)
Tương tự:
\(\frac{B}{2}=\frac{7}{38.31}+\frac{5}{38.43}+\frac{3}{43.46}+\frac{11}{46.57}=\frac{38-31}{38.31}+\frac{41-38}{38.41}+\frac{46-43}{43.46}+\frac{57-46}{46.57}\)
\(=\frac{1}{31}-\frac{1}{38}+\frac{1}{38}-\frac{1}{43}+\frac{1}{43}-\frac{1}{46}+\frac{1}{46}-\frac{1}{57}\)
\(\Rightarrow\frac{B}{2}=2\cdot\left(\frac{1}{31}-\frac{1}{57}\right)\)
Từ đó, suy ra:
\(\frac{A}{B}=\frac{5}{2}\)
Vậy \(\frac{A}{B}=\frac{5}{2}\)
Trl:
\(\frac{A}{5}=\frac{4}{35.31}+\frac{6}{35.41}+\frac{9}{50.41}+\frac{7}{50.57}=\frac{35-31}{35.31}+\frac{41-35}{35.31}+\frac{50-41}{50.41}+\frac{57-50}{50.57}\)
\(\frac{A}{5}=\frac{1}{31}-\frac{1}{35}+\frac{1}{35}-\frac{1}{41}+\frac{1}{41}-\frac{1}{50}+\frac{1}{50}-\frac{1}{57}=\frac{1}{31}-\frac{1}{57}\Rightarrow A=5\left(\frac{1}{31}-\frac{1}{57}\right)\)
\(\frac{B}{2}=\frac{7}{38.31}+\frac{5}{38.43}+\frac{3}{43.46}+\frac{11}{46.57}=\frac{38-31}{31.38}+\frac{43-38}{38.43}+\frac{46-43}{43.46}+\frac{57-46}{46.57}\)
\(\frac{B}{2}=\frac{1}{31}-\frac{1}{38}+\frac{1}{38}-\frac{1}{43}+\frac{1}{43}-\frac{1}{46}+\frac{1}{46}-\frac{1}{57}=\frac{1}{31}-\frac{1}{57}\Rightarrow B=2\left(\frac{1}{31}-\frac{1}{57}\right)\)
\(\Rightarrow\frac{A}{B}=\frac{5}{2}\)
Vậy A/B = 5/2
