(\(\dfrac{617}{191}\) + \(\dfrac{29}{33}\) - \(\dfrac{115}{117}\))(\(\dfrac{1}{4}\) + \(\dfrac{-1}{5}\) - \(\dfrac{1}{20}\))
Tính một cách hợp lí:
a) \(\left(\dfrac{617}{191}+\dfrac{29}{33}-\dfrac{115}{117}\right).\left(\dfrac{1}{4}-\dfrac{1}{5}-\dfrac{1}{20}\right);\)
b) \(\dfrac{12}{5}\cdot\left(\dfrac{10}{3}-\dfrac{5}{12}\right);\)
c) 1,23 - 5,48 + 8,77 - 4,32;
d) 7.0,25 + 9.0,25.
a) Ta có: \(\left(\dfrac{617}{191}+\dfrac{29}{33}-\dfrac{115}{17}\right)\cdot\left(\dfrac{1}{4}-\dfrac{1}{5}-\dfrac{1}{20}\right)\)
\(=\left(\dfrac{617}{191}+\dfrac{29}{33}-\dfrac{115}{17}\right)\cdot\left(\dfrac{5}{20}-\dfrac{4}{20}-\dfrac{1}{20}\right)\)
\(=0\cdot\left(\dfrac{617}{191}+\dfrac{29}{33}-\dfrac{115}{17}\right)=0\)
b) Ta có: \(\dfrac{12}{5}\cdot\left(\dfrac{10}{3}-\dfrac{5}{12}\right)\)
\(=\dfrac{12}{5}\cdot\left(\dfrac{40}{12}-\dfrac{5}{12}\right)\)
\(=\dfrac{12}{5}\cdot\dfrac{35}{12}\)
=7
c) Ta có: \(1.23-5.48+8.77-4.32\)
\(=\left(1.23+8.77\right)-\left(5.48+4.32\right)\)
=10-10=0
Tính giá trị biểu thức sau :
a) A = \(3\dfrac{1}{117}.4\dfrac{1}{119}-1\dfrac{116}{117}.5\dfrac{118}{119}-\dfrac{5}{119}\)
b) B = \(4\dfrac{1}{115}.3\dfrac{1}{225}-5\dfrac{114}{115}.1\dfrac{224}{225}-\dfrac{10}{225}\)
(617/191+29/33-115/117)x(1/4-1/5-1/20)
(617/191+29/33-115/117)*(1/4-1/5-1/20)
= (617/191+29/33-115/117)*(5/20-4/20-1/20)
=(617/191+29/33-115/117)*0
=0
\(\left(\dfrac{617}{191}+\dfrac{29}{33}-\dfrac{115}{117}\right)\times\left(\dfrac{1}{4}-\dfrac{1}{5}-\dfrac{1}{20}\right)\\ =\left(\dfrac{617}{191}+\dfrac{29}{33}-\dfrac{115}{117}\right)\times0\\ =0\)
Tính C= \(3\dfrac{1}{117}\cdot4\dfrac{1}{119}\cdot-1\dfrac{117}{116}\cdot5\dfrac{115}{119}+\dfrac{5}{119}-\dfrac{10}{117}\)
Sửa đề: \(C=3\dfrac{1}{117}.4\dfrac{1}{119}-1\dfrac{116}{117}.5\dfrac{118}{119}+\dfrac{5}{119}-\dfrac{10}{117}\)
\(=\left(3+\dfrac{1}{117}\right)\left(4+\dfrac{1}{119}\right)-\left(1+1-\dfrac{1}{117}\right)\left(5+1-\dfrac{1}{110}\right)+5.\dfrac{1}{119}-10.\dfrac{1}{117}\)
\(=\left(3+\dfrac{1}{117}\right)\left(4+\dfrac{1}{119}\right)-\left(2-\dfrac{1}{117}\right)\left(6-\dfrac{1}{119}\right)+5.\dfrac{1}{119}-10.\dfrac{1}{117}\)
Đặt \(a=\dfrac{1}{117}\) và \(b=\dfrac{1}{119}\) ta có:
\(C=\left(3+a\right).\left(4+b\right)-\left(2-a\right)\left(6-b\right)+5b-10a\)
\(=12+3b+4a+ab-12+2b+6a-ab+5b-10a\)
\(=10b=10.\dfrac{1}{119}=\dfrac{10}{119}\)
tính một cách hợp lí:
a) \(\dfrac{-5}{18}+\dfrac{32}{45}-\dfrac{9}{10}\)
b) \(\left(\dfrac{-1}{4}+\dfrac{51}{33}-\dfrac{5}{3}\right)-\left(\dfrac{-15}{12}+\dfrac{6}{11}-\dfrac{42}{29}\right)\)
c) \(1-\dfrac{1}{2}+2-\dfrac{2}{3}+3-\dfrac{3}{4}+4-\dfrac{1}{4}-3-\dfrac{1}{3}-2-\dfrac{1}{2}-1\)
giải chi tiết giúp mình nha
a) Ta có: \(\dfrac{-5}{18}+\dfrac{32}{45}-\dfrac{9}{10}\)
\(=\dfrac{-25}{90}+\dfrac{64}{90}-\dfrac{81}{90}\)
\(=\dfrac{-42}{90}=-\dfrac{7}{15}\)
b) Ta có: \(\left(-\dfrac{1}{4}+\dfrac{51}{33}-\dfrac{5}{3}\right)-\left(-\dfrac{15}{12}+\dfrac{6}{11}-\dfrac{42}{29}\right)\)
\(=\dfrac{-1}{4}+\dfrac{17}{11}-\dfrac{5}{3}+\dfrac{5}{4}-\dfrac{6}{11}+\dfrac{42}{29}\)
\(=\dfrac{-5}{3}+\dfrac{42}{29}\)
\(=\dfrac{-145}{87}+\dfrac{126}{87}=\dfrac{-19}{87}\)
c) Ta có: \(1-\dfrac{1}{2}+2-\dfrac{2}{3}+3-\dfrac{3}{4}+4-\dfrac{1}{4}-3-\dfrac{1}{3}-2-\dfrac{1}{2}-1\)
\(=\left(1-1\right)-\left(\dfrac{1}{2}+\dfrac{1}{2}\right)+\left(2-2\right)-\left(\dfrac{2}{3}+\dfrac{1}{3}\right)+\left(3-3\right)-\left(\dfrac{3}{4}+\dfrac{1}{4}\right)+4\)
\(=-1-1-1+4\)
=1
a) Ta có: =−2590+6490−8190=−2590+6490−8190
(−14+5133−53)−(−1512+611−4229)(−14+5133−53)−(−1512+611−4229)
=−53+4229=−53+4229
1−12+2−23+3−34+4−14−3−13−2−12−11−12+2−23+3−34+4−14−3−13−2−12−1
GIẢI PHƯƠNG TRÌNH
1)\(\dfrac{x+1}{35}+\dfrac{x+3}{33}=\dfrac{x+5}{31}+\dfrac{x+7}{29}\)
2)x(x+1)(x+2)(x+3)=24
3)\(\dfrac{x-1}{13}-\dfrac{2x-13}{15}=\dfrac{3x-15}{27}-\dfrac{4x-27}{29}\)
4)\(\dfrac{1909-x}{91}+\dfrac{1907-x}{93}+\dfrac{1905-x}{95}+\dfrac{1903-x}{91}+4=0\)
1) PT \(\Leftrightarrow\left(\dfrac{x+1}{35}+1\right)+\left(\dfrac{x+3}{33}+1\right)=\left(\dfrac{x+5}{31}+1\right)+\left(\dfrac{x+7}{29}+1\right)\)
\(\Leftrightarrow\dfrac{x+36}{35}+\dfrac{x+36}{33}=\dfrac{x+36}{31}+\dfrac{x+36}{29}\)
\(\Leftrightarrow\left(x+36\right)\left(\dfrac{1}{29}+\dfrac{1}{31}-\dfrac{1}{33}-\dfrac{1}{35}\right)=0\)
\(\Leftrightarrow x+36=0\) (Do \(\dfrac{1}{29}+\dfrac{1}{31}-\dfrac{1}{33}-\dfrac{1}{35}>0\))
\(\Leftrightarrow x=-36\).
Vậy nghiệm của pt là x = -36.
2) x(x+1)(x+2)(x+3)= 24
⇔ x.(x+3) . (x+2).(x+1) = 24
⇔(\(x^2\) + 3x) . (\(x^2\) + 3x + 2) = 24
Đặt \(x^2\)+ 3x = b
⇒ b . (b+2)= 24
Hay: \(b^2\) +2b = 24
⇔\(b^2\) + 2b + 1 = 25
⇔\(\left(b+1\right)^2\)= 25
+ Xét b+1 = 5 ⇒ b=4 ⇒ \(x^2\)+ 3x = 4 ⇒ \(x^2\)+4x-x-4=0 ⇒x(x+4)-(x+4)=0
⇒(x-1)(x+4)=0⇒x=1 và x=-4
+ Xét b+1 = -5 ⇒ b=-6 ⇒ \(x^2\)+3x=-6 ⇒\(x^2\) + 3x + 6=0
⇒\(x^2\) + 2.x.\(\dfrac{3}{2}\) + (\(\dfrac{3}{2}\))2 = - \(\dfrac{15}{4}\) Hay ( \(x^2\) +\(\dfrac{3}{2}\) )2= -\(\dfrac{15}{4}\) (vô lí)
⇒x= 1 và x= 4
Tính giá trị A= \(3\dfrac{1}{117}.\dfrac{1}{119}-\dfrac{4}{117}.5\dfrac{118}{119}-\dfrac{5}{117.119}+\dfrac{8}{39}\)
Ta có: \(A=3\dfrac{1}{117}\cdot\dfrac{1}{119}-\dfrac{4}{117}\cdot5\dfrac{118}{119}-\dfrac{5}{117\cdot119}+\dfrac{8}{39}\)
\(=\dfrac{352}{117}\cdot\dfrac{1}{119}-\dfrac{4}{117}\cdot\dfrac{713}{119}-\dfrac{5}{117\cdot119}+\dfrac{8}{39}\)
\(=\dfrac{352-2852-5}{117\cdot119}+\dfrac{8}{39}\)
\(=\dfrac{-835}{4641}+\dfrac{8}{39}\)
\(=\dfrac{3}{119}\)
Tính nhanh:
\(\left(\dfrac{67}{111}+\dfrac{2}{33}-\dfrac{15}{117}\right).\left(\dfrac{1}{3}-\dfrac{1}{4}-\dfrac{1}{12}\right)\)
\(\left(\dfrac{67}{111}+\dfrac{2}{33}-\dfrac{15}{117}\right).\left(\dfrac{1}{3}-\dfrac{1}{4}-\dfrac{1}{12}\right)\)
\(=\left(\dfrac{67}{111}+\dfrac{2}{33}-\dfrac{15}{117}\right).\left(\dfrac{4}{12}-\dfrac{3}{12}-\dfrac{1}{12}\right)\)
\(=\left(\dfrac{67}{111}+\dfrac{2}{33}-\dfrac{15}{117}\right).\left(\dfrac{4-3-1}{12}\right)\)
\(=\left(\dfrac{66}{111}+\dfrac{2}{33}+\dfrac{15}{117}\right).0\)
\(=0\)
\(\left(\dfrac{67}{111}+\dfrac{2}{33}-\dfrac{15}{117}\right)\cdot\left(\dfrac{1}{3}-\dfrac{1}{4}-\dfrac{1}{12}\right)\\ =\left(\dfrac{67}{111}+\dfrac{2}{33}-\dfrac{15}{117}\right)\cdot\left(\dfrac{4}{12}-\dfrac{3}{12}-\dfrac{1}{12}\right)\\= \left(\dfrac{67}{111}+\dfrac{2}{33}-\dfrac{15}{117}\right)\cdot\left(\dfrac{4-3-1}{12}\right)\\= \left(\dfrac{67}{111}+\dfrac{2}{33}-\dfrac{15}{117}\right)\cdot0\\ =0\)
\(A=\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{65}+...+\dfrac{1}{99}=\dfrac{16}{x}\)
\(B=\dfrac{5}{6}+\dfrac{11}{12}+\dfrac{19}{20}+\dfrac{29}{30}+\dfrac{41}{42}+\dfrac{55}{56}+\dfrac{x}{16}\)\(C=\left(1-\dfrac{1}{4}\right)\times\left(1-\dfrac{1}{9}\right)\times\left(1-\dfrac{1}{16}\right)\times...\times\left(1-\dfrac{1}{100}\right)=\dfrac{22}{x}\)
m.ng giúp em với
a: \(\Leftrightarrow\dfrac{32}{x}=\dfrac{2}{15}+\dfrac{2}{35}+...+\dfrac{2}{99}\)
=>32/x=1/3-1/5+1/5-1/7+...+1/9-1/11
=>32/x=1/3-1/11=8/33
=>x=32:8/33=132
b: \(\Leftrightarrow1-\dfrac{1}{6}+1-\dfrac{1}{12}+...+1-\dfrac{1}{56}=\dfrac{x}{16}\)
\(\Leftrightarrow6-\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{7}-\dfrac{1}{8}\right)=\dfrac{x}{16}\)
=>x/16=6-1/2+1/8=11/2+1/8=45/8=90/16
=>x=90
c: \(\Leftrightarrow\dfrac{22}{x}=\left(1-\dfrac{1}{2}\right)\left(1+\dfrac{1}{2}\right)\cdot\left(1-\dfrac{1}{3}\right)\left(1+\dfrac{1}{3}\right)\cdot...\cdot\left(1-\dfrac{1}{10}\right)\left(1+\dfrac{1}{10}\right)\)
=>22/x=1/2*2/3*...*9/10*3/2*4/3*...*11/10
=>22/x=1/10*11/2=11/20=22/40
=>x=40