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a, \(\left(\dfrac{3}{7}+\dfrac{1}{2}\right)^2=\left(\dfrac{3}{7}\right)^2+2.\dfrac{3}{7}.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2\)
\(=\dfrac{9}{49}+\dfrac{3}{7}+\dfrac{1}{4}=\dfrac{169}{196}\)
b, \(\left(\dfrac{3}{4}-\dfrac{5}{6}\right)^2=\left(\dfrac{3}{4}\right)^2-2.\dfrac{3}{4}.\dfrac{5}{6}+\left(\dfrac{5}{6}\right)^2\)
\(=\dfrac{9}{16}-\dfrac{5}{4}+\dfrac{25}{36}=\dfrac{1}{144}\)
c, \(\dfrac{5^4.20^4}{25^5.4^5}=\dfrac{5^4.5^4.4^4}{5^{10}.4^5}=\dfrac{1}{5^2.4}=\dfrac{1}{100}\)
d, \(\left(\dfrac{-10}{3}\right)^5.\left(\dfrac{-6}{5}\right)^4=\dfrac{\left(-10\right)^5}{3^5}.\dfrac{6^4}{5^4}\)
\(=\dfrac{5^5.\left(-2\right)^5.2^4.3^4}{3^5.5^4}=\dfrac{-\left(5.2^9\right)}{3}=\dfrac{-2560}{3}\)
Chúc bạn học tốt!!!
b) \(\dfrac{7}{15}-\dfrac{9}{19}\)\(-\dfrac{-8}{15}-\dfrac{10}{19}\)
=\(\left(\dfrac{7}{15}-\dfrac{8}{15}\right)\) \(-\left(\dfrac{9}{19}-\dfrac{10}{19}\right)\)
= \(-\dfrac{1}{15}\) - \(\left(-\dfrac{1}{19}\right)\)
\(=-\dfrac{1}{15}\) + \(\dfrac{1}{19}\)
= \(-\dfrac{4}{285}\)
c) \(1\dfrac{1}{3}\) \(\div\) \(\dfrac{4}{5}\) + 2\(\dfrac{2}{3}\) \(\div\)\(\dfrac{4}{5}\)
= \(\left(1\dfrac{1}{3}+2\dfrac{2}{3}\right)\) \(\div\dfrac{4}{5}\)
= \(\left[\left(1+2\right)+\left(\dfrac{1}{3}+\dfrac{2}{3}\right)\right]\) \(\div\dfrac{4}{5}\)
= ( 3 + 1 ) \(\div\dfrac{4}{5}\)
= 4 \(\div\dfrac{4}{5}\)
= \(\dfrac{4.5}{4}\)
= 5
Bài 7:
x/1=z/2 nên x/6=z/12
=>x/6=y/9=z/12
=>x/2=y/3=z/4
Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:
\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}=\dfrac{x+y+z}{2+3+4}=\dfrac{27}{9}=3\)
=>x=6; y=9; z=12
a/ \(19\dfrac{1}{3}.\dfrac{3}{7}-33\dfrac{1}{3}\)
\(=\dfrac{58}{3}.\dfrac{3}{7}-\dfrac{100}{3}\)
\(=\dfrac{58}{7}-\dfrac{100}{3}\)
\(=\dfrac{-526}{21}\)
b/ \(9.\left(\dfrac{-1}{2}\right)^2+\dfrac{1}{3}\)
\(=9.\dfrac{1}{4}+\dfrac{1}{3}\)
\(=\dfrac{9}{4}+\dfrac{1}{3}=\dfrac{31}{12}\)
c/ \(15\dfrac{1}{4}:\left(-\dfrac{5}{7}\right)-25\dfrac{1}{4}:\left(-\dfrac{5}{7}\right)\)
\(=\dfrac{61}{4}:\left(-\dfrac{5}{7}\right)-\dfrac{101}{4}:\left(-\dfrac{5}{7}\right)\)
\(=\left(-\dfrac{427}{20}\right)-\left(-\dfrac{707}{20}\right)\)
\(=14\)
a: =>1/6x=-49/60
=>x=-49/60:1/6=-49/60*6=-49/10
b: =>3/2x-1/5=3/2 hoặc 3/2x-1/5=-3/2
=>x=17/15 hoặc x=-13/15
c: =>1,25-4/5x=-5
=>4/5x=1,25+5=6,25
=>x=125/16
d: =>2^x*17=544
=>2^x=32
=>x=5
i: =>1/3x-4=4/5 hoặc 1/3x-4=-4/5
=>1/3x=4,8 hoặc 1/3x=-0,8+4=3,2
=>x=14,4 hoặc x=9,6
j: =>(2x-1)(2x+1)=0
=>x=1/2 hoặc x=-1/2
1,\(\dfrac{a}{b}=\dfrac{x}{y}\) khi ay=bx
2,
a,x=\(\dfrac{-1.12}{4}\)
x=\(\dfrac{-12}{4}=-3\)
b,\(\left(\dfrac{1}{3}\right)^{2x-1}=\left(\dfrac{1}{3}\right)^5\)
\(\Rightarrow\)2x-1=5
2x=6
x=6:2=3
c,\(\dfrac{4}{7}\).x=\(\dfrac{1}{5}+\dfrac{2}{3}\)
\(\dfrac{4}{7}.x=\dfrac{3}{15}+\dfrac{10}{15}\)
\(\dfrac{4}{7}.x=\dfrac{13}{15}\)
\(x=\dfrac{13}{15}:\dfrac{4}{7}\)
x=\(\dfrac{13}{15}.\dfrac{7}{4}=\dfrac{91}{60}\)
3,ta có:\(5^{202}=\left(5^2\right)^{101}\)=\(25^{101}\)
2\(^{505}\)=\(\left(2^5\right)^{101}\)=\(32^{101}\)
vì 25<32 nên \(25^{101}< 32^{101}\) hay \(5^{202}< 2^{505}\)
1) \(\dfrac{a}{b}=\dfrac{x}{y}\) khi \(a.y=b.x\)
2) \(a,\dfrac{x}{12}=\dfrac{-1}{4}\)
\(\Rightarrow4x=-12\)
\(\Rightarrow x=-\dfrac{12}{4}=-3\)
Vậy x = -3
\(b,\left(\dfrac{1}{3}\right)^{2x-1}=\dfrac{1}{243}\)
\(\left(\dfrac{1}{3}\right)^{2x-1}=\left(\dfrac{1}{3}\right)^5\)
\(\Rightarrow2x-1=5\)
\(\Rightarrow x=\dfrac{5-1}{2}=2\)
Vậy x = 2
\(c,\dfrac{4}{7}x-\dfrac{2}{3}=\dfrac{1}{5}\)
\(\dfrac{4}{7}x=\dfrac{1}{5}+\dfrac{2}{3}\)
\(\dfrac{4}{7}x=\dfrac{13}{15}\)
\(\Rightarrow x=\dfrac{13}{15}:\dfrac{4}{7}=1\dfrac{31}{60}\)
Vậy \(x=1\dfrac{31}{60}\)
3) So sánh \(5^{202}\) và \(2^{505}\)
\(5^{202}=\left(5^2\right)^{101}=25^{101}\)
\(2^{505}=\left(2^5\right)^{101}=32^{101}\)
\(\Rightarrow25^{101}< 32^{101}\)
\(\Rightarrow5^{202}< 2^{505}\)
2) -12:\(\left(-\dfrac{5}{6}\right)^2\)=\(-12:\dfrac{25}{36}=-12\cdot\dfrac{36}{25}=-\dfrac{432}{25}\)
s) \(-\dfrac{1}{12}-\left(2\dfrac{5}{8}-\dfrac{1}{3}\right)=-\dfrac{1}{12}-\left(\dfrac{21}{8}-\dfrac{1}{3}\right)\)
= \(-\dfrac{1}{12}-\dfrac{55}{24}=-\dfrac{2}{24}-\dfrac{55}{24}=-\dfrac{57}{24}=-\dfrac{19}{8}\)
t) \(-1,75-\left(-\dfrac{1}{9}-2\dfrac{1}{18}\right)=-1,75-\left(-\dfrac{2}{18}-\dfrac{37}{18}\right)\)
= -1,75-(\(-\dfrac{13}{6}\)) = \(-\dfrac{7}{4}+\dfrac{13}{6}=\dfrac{5}{12}\)
c) \(\left(\sqrt{\dfrac{1}{9}}-0,5\right)^3+\dfrac{-1}{3}=\left(\dfrac{1}{3}-\dfrac{1}{2}\right)^3-\dfrac{1}{3}\)
= \(\left(-\dfrac{1}{6}\right)^3-\dfrac{1}{3}=\dfrac{-1}{216}-\dfrac{1}{3}=-\dfrac{73}{216}\)
d) \(\left(\dfrac{1}{2}-\sqrt{\dfrac{4}{25}}\right)^2-2\dfrac{1}{2}=\left(\dfrac{1}{2}-\dfrac{2}{5}\right)^2-\dfrac{5}{2}\)
= \(\left(\dfrac{1}{10}\right)^2-\dfrac{5}{2}=\dfrac{1}{100}-\dfrac{250}{100}=-\dfrac{249}{100}=-2,49\)
= ( 10/15-7/15 ) : ( 10/15 - 6/15)2
= 3/15 : (4/15)2 = 3/15 . (15/4)2
= (3.152)/(15.42) rút gọn 15 trên và dưới
= (3.15)/42 =45/16