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Bài 1 : \(\frac{2}{3}< \left[\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{4}{96}\right]:5\times x< \frac{5}{6}\)
=> \(\frac{2}{3}< \left[\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{1}{24}\right]:5\cdot x< \frac{5}{6}\)
=> \(\frac{2}{3}< \left[\frac{1}{6}+\frac{1}{24}+\frac{2}{15}+\frac{3}{40}\right]:5\cdot x< \frac{5}{6}\)
=> \(\frac{2}{3}< \frac{5}{12}:5\cdot x< \frac{5}{6}\)
=> \(\frac{2}{3}< \frac{1}{12}\cdot x< \frac{5}{6}\)
=> \(\frac{2}{3}< \frac{x}{12}< \frac{5}{6}\)
=> \(\frac{8}{12}< \frac{x}{12}< \frac{10}{12}\)
=> x = 9
Bài 2 : \(\frac{\left[\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right]}{x}=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{132}\)
=> \(\frac{\left[1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}\right]}{x}=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{11\cdot12}\)
=> \(\frac{\left[1-\frac{1}{16}\right]}{x}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{11}-\frac{1}{12}\)
=> \(\frac{15}{\frac{16}{x}}=1-\frac{1}{12}\)
=> \(\frac{15}{\frac{16}{x}}=\frac{11}{12}\)
=> \(\frac{15}{16}:x=\frac{11}{12}\)
=> \(x=\frac{45}{44}\)
Bài 3 : \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\times(x+1):2}=\frac{399}{400}\)
=> \(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\times(x+1)}=\frac{399}{400}\)
=> \(2\left[\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\times(x+1)}\right]=\frac{399}{400}\)
=> \(2\left[\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{x\times(x+1)}\right]=\frac{399}{400}\)
=> \(\left[\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}\right]=\frac{399}{800}\)
=> \(\frac{1}{2}-\frac{1}{x+1}=\frac{399}{800}\)
=> \(\frac{1}{x+1}=\frac{1}{800}\)
=> x = 799
Bài 2 :
\(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right):x=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{132}\) (*)
Ta có : \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}=\frac{8}{16}+\frac{4}{16}+\frac{2}{16}+\frac{1}{16}=\frac{8+4+2+1}{16}=\frac{15}{16}\) (1)
Lại có : \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{132}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{11.12}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{11}-\frac{1}{12}\)
\(=1\left(-\frac{1}{2}+\frac{1}{2}\right)+\left(-\frac{1}{3}+\frac{1}{3}\right)+...+\left(-\frac{1}{11}+\frac{1}{11}\right)-\frac{1}{12}\)
\(=1-\frac{1}{12}=\frac{11}{12}\) (2)
Thay (1) và (2) vào biểu thức (*) ta được :
\(\frac{15}{16}:x=\frac{11}{12}\)
\(\Leftrightarrow x=\frac{15}{16}:\frac{11}{12}\)
\(\Leftrightarrow x=\frac{45}{44}\)
Vậy : \(x=\frac{45}{44}\)
( 2003 - 123 x 8 : 4 ) x ( 36 : 6 - 6 )
= ( 2003 - 123 x 8 : 4 ) x ( 6 - 6 )
= ( 2003 - 123 x 8 : 4 ) x 0
= 0
Chúc bạn học tốt !
\(\text{( 2003 - 123 x 8 : 4 ) x ( 36 : 6 - 6 )}\)
=\(\text{( 2003 - 123 x 8 : 4 ) x (6 - 6 )}\)
=\(\text{( 2003 - 123 x 8 : 4 ) x}0\)
\(=0\)
học tốt
A) X+ X + X + X + X = 5
X x 5 = 5
X = 5 : 5
X = 1
B) X + X + X + X + X = 10
X x 5 = 10
X = 10 : 5
X = 2
A)X + X + X + X + X = 5
X × 5 = 5
X = 5 : 5
X = 1
B) X + X + X + X + X = 10
X × 5 = 10
X = 10 : 5
X = 2
\(\frac{49\cdot63}{14\cdot54}\) \(=\frac{7\cdot7\cdot7\cdot9}{7\cdot2\cdot6\cdot9}\) \(=\) \(\frac{7\cdot7}{2\cdot6}\) \(=\frac{49}{12}\)
Gọi số có 2 chữ số là ab (a,b là số tự nhiên, a khác 0)
Ta có Xab = 3 x ab
100 x X+ab=3 x ab
100 x X= 2 x ab
50 x X= ab
Mà ab là số có 2 chữ số => ab=50 , X=1
Tị ck nha
85 x 72,5 + 15 x 72,5
= 72,5 x ( 85 + 15 )
= 72,5 x 100
= 72,500
(96 ÷ 0,5 - 30 ÷ 0,2 - 84 × 0,5) × (45,5 × 2,98 × 13,4 × 50,04)
= (96 × 2 - 30 × 5 - 84 ÷ 2) × ("viết lại")
= (192 - 150 - 42) × (...)
= (42 - 42) × (...)
= 0 × (...)
= 0
\(17,4\cdot2\cdot15-3,48\cdot6\cdot10+17,4:0,5\)
\(=17,4\cdot2\cdot15-17,4\cdot2\cdot6+17,4\cdot2\)
\(=17,4\cdot2\left(15-6+1\right)\)
\(=34,8\cdot10=348\)
#Louis
17,4 x 2 x 15 - 3,48 x 6 x 10 + 17,4 : 0,5
=17,4x30-3,48x6x5x2+17,4x2
=17,4x30-17,4x6x2+17,4x2
=17,4x(30-6x2+2)
=17,4x20
=348