Tinh bang cach thuan tien:
a) \(1\dfrac{1}{2}x1\dfrac{1}{3}x1\dfrac{1}{4}\)
b) \(1\dfrac{1}{2}:1\dfrac{1}{3}:1\dfrac{1}{4}\)
\(1\dfrac{1}{2}x1\dfrac{1}{3}x1\dfrac{1}{4}x1\dfrac{1}{5}x1\dfrac{1}{6}x1\dfrac{1}{7}x1\dfrac{1}{8}x1\dfrac{1}{9}\)
làm nhanh giúp mik mik cần gấp
\(1\dfrac{1}{2}x1\dfrac{1}{3}x1\dfrac{1}{4}x1\dfrac{1}{5}x1\dfrac{1}{6}x1\dfrac{1}{7}x1\dfrac{1}{8}x1\dfrac{1}{9}\)
\(=\dfrac{3}{2}x\dfrac{4}{3}x\dfrac{5}{4}x\dfrac{6}{5}x\dfrac{7}{6}x\dfrac{8}{7}x\dfrac{9}{8}x\dfrac{10}{9}\)
\(=x^7.\dfrac{3.4.5.6.7.8.9.10}{2.3.4.5.6.7.8.9}\)
\(=x^7.\dfrac{10}{2}\)
\(=5x^7\)
\(=\dfrac{3}{2}\times\dfrac{4}{3}\times\dfrac{5}{4}\times...\times\dfrac{9}{8}\times\dfrac{10}{9}=\dfrac{10}{2}=5\)
\(1:\left(1\dfrac{1}{2}x1\dfrac{1}{3}x1\dfrac{1}{4}......x1\dfrac{1}{99}\right)\)
`1:(1 1/2 xx 1 1/3 xx 1 1/4 xx ... xx 1 1/99 )`
`= 1 : (3/2 xx 4/3 xx 5/4 xx ... xx 100/99)`
`= 1 : 100/2`
`= 1 xx 2/100`
`= 2/100`
`=1/50`
Bài 7: (Đề 2) Tính nhanh
\(1\dfrac{1}{2}x1\dfrac{1}{3}x1\dfrac{1}{4}x...x1\dfrac{1}{999}\)
\(...=\dfrac{3}{2}x\dfrac{4}{3}x\dfrac{5}{4}x\dfrac{6}{5}x\dfrac{7}{6}....x\dfrac{1000}{999}\)
\(=\dfrac{1}{2}x\dfrac{1000}{1}=500\)
=3/2x4/3x5/4x....x1000/999
=1/2x1000=500
mình chưa chắc là đúng đâu nhé
Tính giá trị biểu thức :
C = \(1\dfrac{1}{2}x1\dfrac{1}{3}x1\dfrac{1}{4}x...x1\dfrac{1}{100}\)
\(=>C=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot\dfrac{5}{4}.....\cdot\dfrac{101}{100}\)
\(C=\dfrac{3\cdot4\cdot5.......\cdot101}{2\cdot3\cdot4.........\cdot100}\)
\(C=\dfrac{101}{2}\)
\(C=1\dfrac{1}{2}\cdot1\dfrac{1}{3}\cdot1\dfrac{1}{4}\cdot...\cdot1\dfrac{1}{100}\)
\(C=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot\dfrac{5}{4}\cdot...\cdot\dfrac{101}{100}\)
\(C=\dfrac{101}{2}\)
Bài 5: (Đề 2) Tính
a) \(2-1\dfrac{5}{6}+2\dfrac{2}{3}\)=........
b) \(\dfrac{5}{9}x\left(2\dfrac{5}{6}-1\dfrac{2}{3}\right)\)=..........
c)\(1\dfrac{1}{3}:\left(2+1\dfrac{1}{6}:2\dfrac{5}{6}\right)\)=..........
d) \(2\dfrac{3}{5}:\dfrac{3}{4}x1\dfrac{4}{5}\) =..........
` a/`
` 2 - 1 5/6 + 2 2/3 = 2 - 11/6 - 8/3 = 1/6+ 8/3 = 1/6 + 16/6 = 17/6 `
`b/`
`5/9 xx ( 2 5/6 - 1 2/3 ) = 5/9 xx ( 17/6 - 5/3 ) = 5/9 xx 7/6 = 35/54 `
`c/`
` 1 1/3 : ( 2 + 1 1/6 : 2 5/6 ) `
`= 4/3 : ( 2 + 7/6 : 17/6 ) `
`= 4/3 : ( 2 + 7/6 xx 6/17 )`
`= 4/3 : ( 2 + 7/17 ) `
`= 4/3 : ( 34/17 + 7/17 ) `
`= 4/3 : 41/17 `
`= 4/3 xx 17/41 `
`= 68/123`
` d/`
` 2 3/5 : 3/4 xx 1 4/5 = 13/5 xx 4/3 xx 9/5 =52/15 xx 9/5 = 156/25`
Tìm x
1) \(\sqrt{\dfrac{3x-1}{x+2}}=2\)
2)\(\sqrt{\dfrac{5x-7}{2x- 1}}=2\)
3)\(\dfrac{\sqrt{x}-2}{\sqrt{x}+1}=\dfrac{\sqrt{x}-1}{\sqrt{x}+3}\)
4) \(\dfrac{\sqrt{x}-3}{\sqrt{x}+2}=\dfrac{\sqrt{x}-2}{\sqrt{x}+1}\)
1: \(\Leftrightarrow\dfrac{3x-1}{x+2}=4\)
=>4x+8=3x-1
=>x=-9
2: \(\Leftrightarrow\dfrac{5x-7}{2x-1}=4\)
=>8x-4=5x-7
=>3x=-3
=>x=-1
3: ĐKXD: x>=0
\(PT\Leftrightarrow\left(\sqrt{x}-2\right)\left(\sqrt{x}+3\right)=\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)\)
=>\(x+\sqrt{x}-6=x-1\)
=>căn x=-1+6=5
=>x=25
4: ĐKXĐ: x>=0
PT =>\(\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)=\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)\)
=>x-2*căn x-3=x-4
=>-2căn x-3=-4
=>2căn x+3=4
=>2căn x=1
=>căn x=1/2
=>x=1/4
1\(\dfrac{1}{3}\)x1\(\dfrac{1}{8}\)x1\(\dfrac{1}{15}\)x1\(\dfrac{1}{24}\)x1\(\dfrac{1}{35}\)
\(1\dfrac{1}{3}\times1\dfrac{1}{8}\times1\dfrac{1}{15}\times1\dfrac{1}{24}\times1\dfrac{1}{35}\)
= \(\dfrac{4}{3}\times\dfrac{9}{8}\times\dfrac{16}{15}\times\dfrac{25}{24}\times\dfrac{36}{35}\)
= \(\dfrac{4\times9\times16\times25\times36}{3\times8\times15\times24\times35}\)
= \(\dfrac{1\times2\times2\times25\times36}{1\times2\times15\times24\times35}\)
= \(\dfrac{4\times25\times36}{30\times24\times35}\)
= \(\dfrac{1\times25\times36}{30\times6\times35}=\dfrac{1}{7}\)
\(1\dfrac{1}{3}\times1\dfrac{1}{8}\times1\dfrac{1}{15}\times1\dfrac{1}{24}\times1\dfrac{1}{35}\)
\(=\dfrac{4}{3}\times\dfrac{9}{8}\times\dfrac{16}{15}\times\dfrac{25}{24}\times\dfrac{36}{35}\)
\(=\dfrac{2\times2}{1\times3}\times\dfrac{3\times3}{2\times4}\times\dfrac{4\times4}{3\times5}\times\dfrac{5\times5}{4\times6}\times\dfrac{6\times6}{5\times7}\)
\(=\left(\dfrac{2}{1}\times\dfrac{3}{2}\times\dfrac{4}{3}\times\dfrac{5}{4}\times\dfrac{6}{5}\right)\times\left(\dfrac{2}{3}\times\dfrac{3}{4}\times\dfrac{4}{5}\times\dfrac{5}{6}\times\dfrac{6}{7}\right)\)
\(=6\times\dfrac{2}{7}=\dfrac{12}{7}\)
Giá trị của biểu thức: 2\(\dfrac{3}{5}\)x\(\dfrac{1}{4}\)x1\(\dfrac{1}{2}\)
= 13/5 x 1/4 x 3/2
= 13 x 1 x 3/ 5 x 4 x 2
= 39/40
= \(\dfrac{13}{5}\)x\(\dfrac{1}{4}\)x\(\dfrac{3}{2}\)
= \(\dfrac{39}{40}\)
Tìm các số x1, x2, x3, x4, x5 biết \(\dfrac{x1-1}{5}=\dfrac{x2-2}{4}=\dfrac{x3-3}{3}=\dfrac{x4-4}{2}=\dfrac{x5-5}{1}vàx1+x2+x3+x4+x5=30\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x_1-1}{5}=\dfrac{x_2-2}{4}=\dfrac{x_3-3}{3}=\dfrac{x_4-4}{2}=\dfrac{x_5-5}{1}\)
\(=\dfrac{\left(x_1-1\right)+\left(x_2-2\right)+\left(x_3-3\right)+\left(x_4-4\right)+\left(x_5-5\right)}{5+4+3+2+1}\)
\(=\dfrac{\left(x_1+x_2+x_3+x_4+x_5\right)-\left(1+2+3+4+5\right)}{15}\)
\(=\dfrac{30-15}{15}=1\)
\(\Rightarrow x_1=x_2=x_3=x_4=x_5=6\)
Vậy...
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x1-1}{5}\)=\(\dfrac{x2-2}{4}\)\(\dfrac{x3-3}{3}\)=\(\dfrac{x4-4}{2}\)=\(\dfrac{x5-5}{1}\)=\(\dfrac{x1-1+x2-2+x3-3+x4-4+x5-5}{5+4+3+2+1}\)=\(\dfrac{x1+x2+x3+x4+x5-\left(1+2+3+4+5\right)}{15}\)=\(\dfrac{30-15}{15}\)=\(\dfrac{15}{15}\)=1
\(\dfrac{x1-1}{5}\)=1 => x1-1=5 => x1 =6
\(\dfrac{x2-2}{4}\)=1 => x2-2=4 => x2 =6
\(\dfrac{x3-3}{3}\)=1 => x3-3=3 => x3 =6
\(\dfrac{x4-4}{2}\)=1 => x4-4=2 => x4 =6
\(\dfrac{x5-5}{1}\)=1 => x5-5=1 => x5 = 6
Vậy x1=x2=x3=x4=x5 =6