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\(a)\frac{5}{8}-x=2\frac{1}{6}\)
\(\Rightarrow\frac{5}{8}-x=\frac{13}{6}\)
\(\Rightarrow x=\frac{5}{8}-\frac{13}{6}\)
\(\Rightarrow x=\frac{15}{24}-\frac{52}{24}\)
\(\Rightarrow x=-\frac{37}{24}\)
\(b)\) \(\frac{4}{9}:x=-\frac{1}{3}+1\frac{1}{6}\)
\(\Rightarrow\frac{4}{9}:x=-\frac{1}{3}+\frac{7}{6}\)
\(\Rightarrow\frac{4}{9}:x=-\frac{2}{6}+\frac{7}{6}\)
\(\Rightarrow\frac{4}{9}:x=\frac{5}{6}\)
\(\Rightarrow x=\frac{4}{9}:\frac{5}{6}\)
\(\Rightarrow x=\frac{4}{9}.\frac{6}{5}\)
\(\Rightarrow x=\frac{8}{15}\)
\(c)\left(3x-2\right)^3=-\frac{1}{27}\)
\(\Rightarrow3x-2=-\frac{1}{3}\)
\(\Rightarrow3x=-\frac{1}{3}+2\)
\(\Rightarrow3x=-\frac{1}{3}+\frac{6}{3}\)
\(\Rightarrow3x=\frac{5}{3}\)
\(\Rightarrow x=\frac{5}{3}:3\)
\(\Rightarrow x=\frac{5}{9}\)
d ) và e ) tự làm
Chúc bạn học tốt !!!
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\(\frac{x+1}{19}+\frac{x+2}{18}=\frac{x+3}{17}+\frac{x+4}{16}\)
\(\Rightarrow\left(\frac{x+1}{19}+1\right)+\left(\frac{x+2}{18}+1\right)=\left(\frac{x+3}{17}+1\right)+\left(\frac{x+4}{16}+1\right)\)
\(\Rightarrow\frac{x+20}{19}+\frac{x+20}{18}=\frac{x+20}{17}+\frac{x+20}{16}\)
\(\Rightarrow\frac{x+20}{19}+\frac{x+20}{18}-\frac{x+20}{17}-\frac{x+20}{16}=0\)
\(\Rightarrow\left(x+20\right).\left(\frac{1}{19}+\frac{1}{18}-\frac{1}{17}-\frac{1}{16}\right)=0\)
Vì : \(\frac{1}{19}+\frac{1}{18}-\frac{1}{17}-\frac{1}{16}\ne0\)nên \(x+20=0\)
Suy ra : \(x=0-20=-20\)
Vậy \(x=-20\)
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* Cách làm : Tử giữ nguyên,còn mẫu ta biến đổi như sau:
Mẫu : ( \(\frac{19}{1}\)+ 1 ) + ( \(\frac{18}{2}\)+ 1 ) + ( \(\frac{17}{3}\)+ 1 ) +...+ ( \(\frac{3}{17}\)+ 1 ) + ( \(\frac{2}{18}\)+ 1 ) + ( \(\frac{1}{19}\)+ 1 ) - 19 ( vì ta cộng với 19 số 1 nên phải trừ 19 )
= \(\frac{20}{1}\)+ \(\frac{20}{2}\)+ \(\frac{20}{3}\)+...+ \(\frac{20}{17}\)+ \(\frac{20}{18}\)+ \(\frac{20}{19}\)- 19
= \(\frac{20}{2}\)+ \(\frac{20}{3}\)+...+ \(\frac{20}{17}\)+ \(\frac{20}{18}\)+ \(\frac{20}{19}\)+ ( \(\frac{20}{1}\)- 19)
= \(\frac{20}{2}\)+ \(\frac{20}{3}\)+ ...+ \(\frac{20}{17}\)+ \(\frac{20}{18}\)+ \(\frac{20}{19}\)+ \(\frac{20}{20}\)
= 20.( \(\frac{1}{2}\)+ \(\frac{1}{3}\)+...+ \(\frac{1}{17}\)+ \(\frac{1}{18}\)+ \(\frac{1}{19}\)+ \(\frac{1}{20}\))
=> \(\frac{Tử}{Mâu}\)= \(\frac{1}{20}\)
Phùng Quang Thịnh biến đổi sai 1 chỗ kìa
-19 = \(\frac{20}{20}-20\)chứ mà bạn
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Xét tử:
\(\frac{1}{19}+\frac{2}{18}+\frac{3}{17}+....+\frac{19}{1}\)
= \(\left(1+\frac{1}{19}\right)+\left(1+\frac{2}{18}\right)+\left(1+\frac{3}{17}\right)+.....+\left(1+\frac{18}{2}\right)+1\)
= \(\frac{20}{19}+\frac{20}{18}+\frac{20}{17}+.....+\frac{20}{2}+1\)
= \(\frac{20}{20}+\frac{20}{19}+\frac{20}{18}+\frac{20}{17}+...+\frac{20}{2}\)
= \(20\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{20}\right)\)
Thay vào, ta có:
D = \(\frac{20\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{20}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{20}}\)
=> D = 20
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Tử số = T = \(\frac{1}{19}+\frac{2}{18}+\frac{3}{17}+....+\frac{18}{2}+\frac{19}{1}\)
\(=\left(\frac{1}{19}+1\right)+\left(\frac{2}{18}+1\right)+\left(\frac{3}{17}+1\right)+....+\left(\frac{19}{1}+1\right)-19\)
\(=\frac{20}{19}+\frac{20}{18}+\frac{20}{17}+....+\frac{20}{2}+20-19\)
\(=\frac{20}{2}+\frac{20}{3}+....+\frac{20}{18}+\frac{20}{19}+\frac{20}{20}\)
\(=20\left(\frac{1}{2}+\frac{1}{3}+....+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}\right)\)
= 20.Mẫu số
\(\Rightarrow\frac{\frac{1}{19}+\frac{2}{18}+....+\frac{18}{2}+\frac{19}{1}}{\frac{1}{2}+\frac{1}{3}+....+\frac{1}{19}+\frac{1}{20}}=20\)
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Mẫu số = 1/19 + 2/18 + 3/17 + ... + 18/2 + 19/1
= ( 1/19 + 2/18 + 3/17 + ... + 18/2 ) + ( 1 + 1 + ... + 1 )
( 18 phân số ) ( 19 số 1 )
= ( 1/19 + 1 ) + ( 2/18 + 1) + ( 3/17 +1 ) + ...+ ( 18/2 + 1 ) + 1
= 20/19 + 20/18 + 20/17 + ... + 20/2 + 20/20
= 20 x ( 1/2 + 1/3 + ... + 1/19 + 1/20 )
Vậy phân số trên= 20
Mẫu số = 1/19 + 2/18 + 3/17 + ... + 18/2 + 19/1
= ( 1/19 + 2/18 + 3/17 + ... + 18/2 ) + ( 1 + 1 + ... + 1 )
( 18 phân số ) ( 19 số 1 )
= ( 1/19 + 1 ) + ( 2/18 + 1) + ( 3/17 +1 ) + ...+ ( 18/2 + 1 ) + 1
= 20/19 + 20/18 + 20/17 + ... + 20/2 + 20/20
= 20 x ( 1/2 + 1/3 + ... + 1/19 + 1/20 )
Vậy phân số trên= 20
a. /3x-4/=16+[1/19+18/19]
/3x-4/=16+1
/3x-4/=17
Suy ra 3x-4=17 hoặc -17
-Nếu 3x-4=17 -Nếu 3x-4=-17
3x=17+4 3x =-17+4
3x=21 3x =-13
x=21:3 x =-13:3
x=7 x =-13/3
b./2x+1/=x+2
Suy ra 2x+1=x+2 hoặc -[x+2]
-Nếu 2x+1=x+2 -Nếu 2x+1=-[x+2]
2x =x+2-1 2x+1=-x+[-2]
2x =x+1 2x =-x+[-2]-1
2x-x =1 2x-[- x]=-3
x =1 3x =-3
x =-3:3
x =-1