\(Rutgonphanso:\frac{10+5}{4+5}\) Va \(\frac{2^2x9}{27x2}\)
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CW
23 tháng 7 2016
a) \(\frac{6^7}{4^3\cdot9^2}=\frac{2^7\cdot3^7}{2^6\cdot3^4}=2\cdot3^3=2\cdot27=54\)
b) \(\frac{12^3\cdot15^3}{4^3\cdot25^2\cdot9^2}=\frac{2^6\cdot3^3\cdot3^3\cdot5^3}{2^6\cdot5^4\cdot3^4}=\frac{3^2}{5}=1,8\)
c) \(\frac{2^{11}+3\cdot2^{10}}{10\cdot4^5}=\frac{2^{10}\left(2+3\right)}{2\cdot5\cdot2^{10}}=\frac{1}{2}=0,5\)
d) \(\frac{3^8\cdot2-3^6}{2\cdot17\cdot3^7}=\frac{3^6\left(3^2\cdot2-1\right)}{2\cdot17\cdot3^7}=\frac{1}{2\cdot3}=\frac{1}{6}\)
25 tháng 8 2019
a,\(\left(5+4\sqrt{2}\right)\left(3+2\sqrt{1+\sqrt{2}}\right)\left(3-2\sqrt{1+\sqrt{2}}\right)\)
=\(\left(5+4\sqrt{2}\right)\left(9-4\left(1+\sqrt{2}\right)\right)\)
=\(\left(5+4\sqrt{2}\right)\left(9-4-4\sqrt{2}\right)\)
=\(\left(5+4\sqrt{2}\right)\left(5-4\sqrt{2}\right)=25-\left(4\sqrt{2}\right)^2\)
=-7
b, \(\sqrt{\frac{9}{4}-\sqrt{2}}=\sqrt{\frac{9-4\sqrt{2}}{4}}=\frac{\sqrt{9-4\sqrt{2}}}{2}=\frac{\sqrt{9-2\sqrt{8}}}{2}=\frac{\sqrt{\left(\sqrt{8}-1\right)^2}}{2}=\frac{\left|\sqrt{8}-1\right|}{2}=\frac{\sqrt{8}-1}{2}\)
26 tháng 8 2019
So sánh:
1) \(2\sqrt{27}\) và \(\sqrt{147}\)
+ \(2\sqrt{27}\) = \(6\sqrt{3}\)
+ \(\sqrt{147}\) = \(7\sqrt{3}\)
⇒ \(6\sqrt{3}\) < \(7\sqrt{3}\)
Vậy: \(2\sqrt{27}\)< \(\sqrt{147}\)
2) \(2\sqrt{15}\) và \(\sqrt{59}\)
+ \(2\sqrt{15}\) = \(\sqrt{60}\)
⇒ \(\sqrt{60}\) > \(\sqrt{59}\)
Vậy: \(2\sqrt{15}\) > \(\sqrt{59}\)
3) \(2\sqrt{2}-1\) và 2
\(giống\left(-1\right)\left\{{}\begin{matrix}3-1\\2\sqrt{2}-1\end{matrix}\right.\)
So sánh: 3 và \(2\sqrt{2}\)
+ 3 = \(\sqrt{9}\)
+ \(2\sqrt{2}=\sqrt{8}\)
⇒ \(\sqrt{8}\) < \(\sqrt{9}\)
⇒ \(\sqrt{8}\) -1 < \(\sqrt{9}\) -1
⇒ \(2\sqrt{2}\) - 1 < 3 - 1
Vậy: \(2\sqrt{2}-1< 2\)
4) \(\frac{\sqrt{3}}{2}\) và 1
+ 1 = \(\frac{2}{2}\)
⇒ \(\frac{\sqrt{3}}{2}\) < \(\frac{2}{2}\)
Vậy: \(\frac{\sqrt{3}}{2}\) < 1
5) \(\frac{-\sqrt{10}}{2}\) và \(-2\sqrt{5}\)
+ \(-2\sqrt{5}\) = \(\frac{-4\sqrt{5}}{2}\) = \(\frac{-\sqrt{80}}{2}\)
⇒ \(\frac{-\sqrt{10}}{2}\) > \(\frac{-\sqrt{80}}{2}\)
Vậy: \(\frac{-\sqrt{10}}{2}\) > \(-2\sqrt{5}\)
11 tháng 6 2016
Đặt A = 1/2 - 1/3 - 2/3 + 1/4 + 2/4 + 3/4 - 1/5 - 2/5 - 3/5 - 4/5 + ... + 1/10 + ...+ 9/10
A = 1/2 - ( 1/3 + 2/3) + (1/4 + 2/4 + 3/4) - ( 1/5 + 2/5 + 3/5 + 4/5) + ( 1/6 + 2/6 + ... + 5/6) - ( 1/7 + 2/7 + ... + 6/7) + ( 1/8 + 2/8 + ... + 7/8) - ( 1/9 + 2/9 + ... + 8/9)
A = 1/2 - 1 + [( 1/4 + 3/4) + 2/4] - [(1/5 + 4/5) + (2/5 + 3/5)] + [(1/6+5/6) + ( 2/6 + 4/6) + 3/6] - [(1/7 + 6/7) + (2/7 + 5/7) + (3/7 + 4/7)] + [(1/8 + 7/8) + (2/8 + 6/8) + (3/8 + 5/8) + 4/8)] - [(1/9 + 8/9) + (2/9 + 7/9) + (3/9 + 6/9) + (4/9 + 5/9)] + [(1/10 + 9/10) + ( 2/10 + 8/10) + ( 3/10 + 7/10) + ( 4/10 + 6/10) + 5/10]
A = 1/2 - 1 + ( 1 + 1/2) - 2 + ( 2 + 1/2) - 3 + ( 3 + 1/2) - 4 + ( 4 + 1/2)
A = 1/2 + 1/2 + 1/2 + 1/2 + 1/2
A = 1/2 × 5 = 5/2
15 tháng 6 2016
Đặt A = 1/2 - 1/3 - 2/3 + 1/4 + 2/4 + 3/4 - 1/5 - 2/5 - 3/5 - 4/5 + ... + 1/10 + ...+ 9/10
A = 1/2 - ( 1/3 + 2/3) + (1/4 + 2/4 + 3/4) - ( 1/5 + 2/5 + 3/5 + 4/5) + ( 1/6 + 2/6 + ... + 5/6) - ( 1/7 + 2/7 + ... + 6/7) + ( 1/8 + 2/8 + ... + 7/8) - ( 1/9 + 2/9 + ... + 8/9)
A = 1/2 - 1 + [( 1/4 + 3/4) + 2/4] - [(1/5 + 4/5) + (2/5 + 3/5)] + [(1/6+5/6) + ( 2/6 + 4/6) + 3/6] - [(1/7 + 6/7) + (2/7 + 5/7) + (3/7 + 4/7)] + [(1/8 + 7/8) + (2/8 + 6/8) + (3/8 + 5/8) + 4/8)] - [(1/9 + 8/9) + (2/9 + 7/9) + (3/9 + 6/9) + (4/9 + 5/9)] + [(1/10 + 9/10) + ( 2/10 + 8/10) + ( 3/10 + 7/10) + ( 4/10 + 6/10) + 5/10]
A = 1/2 - 1 + ( 1 + 1/2) - 2 + ( 2 + 1/2) - 3 + ( 3 + 1/2) - 4 + ( 4 + 1/2)
A = 1/2 + 1/2 + 1/2 + 1/2 + 1/2
A = 1/2 × 5 = 5/2
NP
0
HP
8 tháng 8 2016
\(A=\frac{1}{6.10}+\frac{1}{10.14}+\frac{1}{14.18}+\frac{1}{18.22}+\frac{1}{22.26}+\frac{1}{26.30}\)
\(=\frac{1}{4}.\left(\frac{1}{6}-\frac{1}{10}+\frac{1}{10}-\frac{1}{14}+\frac{1}{14}-\frac{1}{18}+\frac{1}{18}-\frac{1}{22}+\frac{1}{22}-\frac{1}{26}+\frac{1}{26}-\frac{1}{30}\right)\)
\(=\frac{1}{4}.\left(\frac{1}{6}-\frac{1}{30}\right)=\frac{1}{4}.\frac{2}{15}=\frac{1}{30}\)
\(B=\frac{5}{2.3}+\frac{5}{3.4}+\frac{5}{4.5}+...+\frac{5}{8.9}\)\(=5.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{8.9}\right)\) \(=5.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{8}-\frac{1}{9}\right)\)
\(=5.\left(\frac{1}{2}-\frac{1}{9}\right)=5.\frac{7}{18}=\frac{35}{18}\)
\(C=\left(\frac{7^2}{2.9}+\frac{7^2}{9.16}+....+\frac{7^2}{65.72}\right):\left(\frac{1}{3}-\frac{7}{36}\right)\)
\(=7.\left(\frac{7}{2.9}+\frac{7}{9.16}+...+\frac{7}{65.72}\right):\frac{5}{36}\) \(=7.\left(\frac{1}{2}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+...+\frac{1}{65}-\frac{1}{72}\right):\frac{5}{36}\)'
\(=7.\left(\frac{1}{2}-\frac{1}{72}\right):\frac{5}{36}=7.\frac{35}{72}:\frac{5}{36}=\frac{49}{2}\)
\(D=\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{37.38.39}+\frac{2}{38.39.40}\)
\(=2.\left(\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{37.38.39}+\frac{1}{38.39.40}\right)\)
\(=2.\frac{1}{2}.\left(\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{37.38}-\frac{1}{38.39}+\frac{1}{38.39}-\frac{1}{39.40}\right)\)
\(=\frac{1}{2.3}-\frac{1}{39.40}=\frac{259}{1560}\)
\(E=\frac{202202}{1212}+\frac{202202}{2020}+\frac{202202}{3030}+\frac{202202}{4242}+\frac{202202}{5656}\)
\(=202202.\left(\frac{1}{3.4.101}+\frac{1}{4.5.101}+\frac{1}{5.6.101}+\frac{1}{6.7.101}+\frac{1}{7.8.101}\right)\)
\(=2002.\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\right)\)
\(=2002.\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\right)\)
\(=2002.\left(\frac{1}{3}-\frac{1}{8}\right)=2002.\frac{5}{24}=\frac{5005}{12}\)
21 tháng 10 2018
Mình làm 1 phép thôi nha những phép còn lại bạn tự nghĩ nhé !
\(\frac{x}{7}=\frac{y}{3}\) và \(x-24=y\)'
Ta có : \(x-24=y\) hay cũng có thể viết \(x-y=24\)
Ta lại có : \(\frac{x}{7}=\frac{y}{3}\)
Áp dụng tính chất của dãy tỉ số bằng nhau nên ta được :
\(\frac{x}{7}=\frac{y}{3}=\frac{x-y}{7-3}=\frac{24}{4}=6\) ( vì \(x-y=24\) )
\(\Rightarrow\frac{x}{7}=6\Rightarrow x=6\cdot7\Rightarrow x=42\)
\(\Rightarrow\frac{y}{3}=6\Rightarrow y=6\cdot3\Rightarrow y=18\)
Vậy \(x=42\) và \(y=18\)