tinh nhanh
\(\frac{4}{3\text{x}7}\)+ \(\frac{5}{7\text{x}12}\)+ \(\frac{1}{12\text{x}13}\)+ \(\frac{7}{13\text{x}20}\)+ \(\frac{3}{20\text{x}23}\)+ \(\frac{6}{23\text{x}29}\)
1) Tính nhanh
a) A=\(\frac{3}{11\text{x}13}+\frac{3}{13\text{x}15}+\frac{3}{15\text{x}17}+...+\frac{3}{97\text{x}99}\)
b) B=\(\frac{4}{7\text{x}31}+\frac{6}{7\text{x}11}+\frac{9}{10\text{x}41}+\frac{7}{10\text{x}57}\)
3) Chứng tỏ phân số \(\frac{8n+5}{6n+4}\)tối giản với mọi số nguyên khác 0
\(A=\frac{3}{2}\times\left(\frac{1}{13\times11}+\frac{1}{13\times15}+\frac{1}{15\times17}+.....+\frac{1}{97\times99}\right)\)
\(A=\frac{3}{2}\times\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+......+\frac{1}{97}-\frac{1}{99}\right)\)
\(A=\frac{3}{2}\times\left(\frac{1}{11}-\frac{1}{99}\right)\)
\(A=\frac{3}{2}\times\frac{8}{99}\)
\(A=\frac{4}{33}\)
b] \(\frac{A}{5}=\frac{4}{31.35}+\frac{6}{35.41}+\frac{9}{41.50}+\frac{7}{50.57}\)
\(\frac{A}{5}=\frac{1}{31}-\frac{1}{35}+\frac{1}{35}-\frac{1}{41}+\frac{1}{41}-\frac{1}{50}+\frac{1}{50}-\frac{1}{57}\)
\(\frac{A}{5}=\frac{1}{31}-\frac{1}{57}\)
\(\Rightarrow A=5\left(\frac{1}{31}-\frac{1}{57}\right)=\frac{130}{1767}\)
c] Ta đặt \(\left(8n+5,6n+4\right)=d\)
\(\Rightarrow\frac{8n+5\div d}{6n+4\div d}\Rightarrow4\times\left(6n+4\right)-3\times\left(8n+5\right)=\left(24n+16\right)-\left(24n+15\right):d\)\(\Rightarrow d=1\)
Vậy \(\frac{8n+5}{6n+4}\)là phân số tối giản
\(\frac{1\text{x}3\text{x}5+2\text{x}6\text{x}10+4\text{x}12\text{x}20+7\text{x}21\text{x}35}{1\text{x}5\text{x}7+2\text{x}10\text{x}14+4\text{x}20\text{x}28+7\text{x}35\text{x}49}\)
( hơi nhỏ xíu )
\(=\frac{1\cdot3\cdot5+2^3\cdot1\cdot3\cdot5+4^3\cdot1\cdot3\cdot5+7^3\cdot1\cdot3\cdot5}{1\cdot5\cdot7+2^3\cdot1\cdot5\cdot7+4^3\cdot1\cdot5\cdot7+7^3\cdot1\cdot5\cdot7}=\frac{1\cdot3\cdot5\cdot\left(1+2^3+4^3+7^3\right)}{1\cdot5\cdot7\cdot\left(1+2^3+4^3+7^3\right)}=\frac{3}{7}\)
a)\(\frac{-2}{3}.x+\frac{1}{5}=\frac{3}{10}\)
b )\(2\frac{7}{9}-\frac{12}{13}x=\frac{7}{9}\)
c)\(\text{|}x\text{|}-\frac{3}{4}=\frac{5}{3}\)
d) \(\frac{17}{2}-\text{|}2x-\frac{3}{4}\text{|}=-\frac{7}{4}\)
a) -2 /3 x + 1/5 = 3/10
-2/3x =1/10
x = -3/20
vậy x = -3/20
b) 25/9 - 12/13x = 7/
12/13x = 2
x = 13/6
c) (x) - 3/4 =5/3
(x) = 29/12
x = 29/12 ; -29/-12
d) x = 11/2
Tìm x biết
a,\(\left(\frac{4}{5}\right)^{2x+7}\text{=}\frac{625}{256}\)
b,\(\frac{7^{x+2}+7^{x+1}+7^x}{57}\text{=}\frac{5^{2x}+5^{2x+1}+5^{2x+3}}{131}\)
c,\(\left(4x-3\right)^4\text{=}\left(4x-3\right)^2\)
d,\(\frac{2x+3}{5x+2}\text{=}\frac{4x+5}{10x+2}\)
e,\(\frac{3x-1}{40-5x}\text{=}\frac{2x-3x}{5x-34}\)
f,\(\frac{15}{x-9}\text{=}\frac{20}{y-12}\text{=}\frac{40}{z-2x}\) và \(xy\text{=}1200\)
a)\(\left(\frac{4}{5}\right)^{2x+7}=\left(\frac{4}{5}\right)^4\)
=> 2x + 7 = 4
2x = 4 - 7
2x = -3
x = -3 : 2
x = -1,5
Vậy x = -1,5
bai 1 \(\frac{-3}{\text{2}}+\frac{5}{7}+\frac{-31}{14}< hoac=\text{x}< \frac{1}{\text{2}}+\frac{1}{3}+\frac{1}{6}\)\(\frac{1}{6}\)
bai 2 \(\frac{\text{x}+4}{\text{x}-\text{2}}+\frac{\text{2}\text{x}-5}{\text{x}-\text{2}}\)la so nguyen
Bài 1 mk ko hiểu đề cho lắm
Bài 2 :
Đặt \(A=\frac{x+4}{x-2}+\frac{2x-5}{x-2}\)
Ta có :
\(\frac{x+4}{x-2}+\frac{2x-5}{x-2}=\frac{x+4+2x-5}{x-2}=\frac{3x-1}{x-2}=\frac{3x-6+5}{x-2}=\frac{3\left(x-2\right)}{x-2}+\frac{5}{x-2}=3+\frac{5}{x-2}\)
Để \(A\) là số nguyên thì \(\frac{5}{x-2}\) phải là số nguyên \(\Rightarrow\) \(5⋮\left(x-2\right)\) \(\Rightarrow\) \(\left(x-2\right)\inƯ\left(5\right)\)
Mà \(Ư\left(5\right)=\left\{1;-1;5;-5\right\}\)
Do đó :
\(x-2\) | \(1\) | \(-1\) | \(5\) | \(-5\) |
\(x\) | \(3\) | \(1\) | \(7\) | \(-3\) |
Vậy \(x\in\left\{-3;1;3;7\right\}\) thì A là số nguyên
Chúc bạn học tốt ~
bai 1: Viết tập hợp A các số nguyên x biết:
cau hoi cua phung minh quan
( Câu siêu khó dành cho học sinh đội tuyển Toán )
( Giúp với )
Bài 10 :
b) \(\frac{\left(\text{13}\frac{\text{1}}{\text{4}}-\text{2}\frac{\text{5}}{\text{27}}-\text{10}\frac{\text{5}}{\text{6}}\right).\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\left(\text{1}\frac{\text{3}}{\text{7}}+\frac{\text{10}}{\text{3}}\right):\left(\text{12}\frac{\text{1}}{\text{3}}-\text{14}\frac{\text{2}}{\text{7}}\right)}\)
\(\frac{\left(\text{13}\frac{\text{1}}{\text{4}}-\text{2}\frac{\text{5}}{\text{27}}-\text{10}\frac{\text{5}}{\text{6}}\right).\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\left(\text{1}\frac{\text{3}}{\text{7}}+\frac{\text{10}}{\text{3}}\right):\left(\text{12}\frac{\text{1}}{\text{3}}-\text{14}\frac{\text{2}}{\text{7}}\right)}=\frac{\left[\text{13}\frac{\text{1}}{\text{4}}-\left(\text{2}\frac{\text{5}}{\text{27}}+\text{10}\frac{\text{5}}{\text{6}}\right)\right].\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{100}}{\text{21}}:\frac{\text{-41}}{\text{21}}}\)
\(=\frac{\left(\text{13}\frac{\text{1}}{\text{4}}-\text{13}\frac{\text{1}}{54}\right).\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}=\frac{\frac{\text{25}}{\text{108}}.\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}\)
\(=\frac{\text{53}\frac{\text{1}}{\text{4}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}=\frac{\text{100}}{\frac{-\text{100}}{\text{41}}}=\text{-41}\)
Giải :
\(\frac{\left(\text{13}\frac{\text{1}}{\text{4}}-\text{2}\frac{\text{5}}{\text{27}}-\text{10}\frac{\text{5}}{\text{6}}\right).\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\left(\text{1}\frac{\text{3}}{\text{7}}+\frac{\text{10}}{\text{3}}\right):\left(\text{12}\frac{\text{1}}{\text{3}}-\text{14}\frac{\text{2}}{\text{7}}\right)}=\frac{\left[\text{13}\frac{\text{1}}{\text{4}}-\left(\text{2}\frac{\text{5}}{\text{27}}+\text{10}\frac{\text{5}}{\text{6}}\right)\right].\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{100}}{\text{21}}:\frac{\text{-41}}{\text{21}}}\)
\(=\frac{\left(\text{13}\frac{\text{1}}{\text{4}}-\text{13}\frac{\text{1}}{54}\right).\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}=\frac{\frac{\text{25}}{\text{108}}.\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}\)
\(=\frac{\text{53}\frac{\text{1}}{\text{4}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}=\frac{\text{100}}{\frac{-\text{100}}{\text{41}}}=\text{-41}\)
~~Học tốt~~
\(\text{Giải :}\)
\(\frac{\left(\text{13}\frac{\text{1}}{\text{4}}-\text{2}\frac{\text{5}}{\text{27}}-\text{10}\frac{\text{5}}{\text{6}}\right).\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\left(\text{1}\frac{\text{3}}{\text{7}}+\frac{\text{10}}{\text{3}}\right):\left(\text{12}\frac{\text{1}}{\text{3}}-\text{14}\frac{\text{2}}{\text{7}}\right)}=\frac{\left[\text{13}\frac{\text{1}}{\text{4}}-\left(\text{2}\frac{\text{5}}{\text{27}}+\text{10}\frac{\text{5}}{\text{6}}\right)\right].\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{100}}{\text{21}}:\frac{\text{-41}}{\text{21}}}\)
\(=\frac{\left(\text{13}\frac{\text{1}}{\text{4}}-\text{13}\frac{\text{1}}{54}\right).\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}=\frac{\frac{\text{25}}{\text{108}}.\text{230}\frac{\text{1}}{\text{25}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}\)
\(=\frac{\text{53}\frac{\text{1}}{\text{4}}+\text{46}\frac{\text{3}}{\text{4}}}{\frac{\text{-100}}{\text{41}}}=\frac{\text{100}}{\frac{-\text{100}}{\text{41}}}=\text{-41}\)
\(\text{~~Học tốt~~}\)
\(\frac{11}{40}+\frac{4}{5}-\text{|}\frac{3}{4}-1\frac{5}{12}\text{|}=\frac{3}{20}-x\)
tính:
\(\frac{\text{x+1}}{10}+\frac{\text{x+1}}{11}-\frac{\text{x+1}}{13}+\frac{\text{x+1}1}{12}-\frac{\text{x+1}}{14}=0\)
Tính
\(\frac{25.\text{4}7-2\text{4}}{23+\text{4}7.2\text{4}}.\frac{\text{4}+\frac{\text{4}}{7}-\frac{\text{4}}{11}+\frac{\text{4}}{2005}-\frac{\text{4}}{13}}{\frac{8}{2005}-\frac{8}{13}+\frac{8}{7}-\frac{8}{11}+8}\)
Cái số bị khuyết là 8 nhé