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Ta co : \(\frac{1}{3}+\frac{1}{31}+\frac{1}{35}+\frac{1}{37}+\frac{1}{47}+\frac{1}{53}+\frac{1}{61}
so sánh
ta có
333444=3334.111=(3334)111
444333=4443.111=(4443)111
So sánh 3334và 4443 ta có
3334=(3.111)4=34 . 1114=81.1114
4443=(4.111)3=43. 1113=64. 1113
Vì 81.1114>64.1113
Suy ra 333444>444333
1.
b) \(3^x+3^{x+2}=2430\)
\(\Rightarrow3^x.1+3^x.3^2=2430\)
\(\Rightarrow3^x.\left(1+3^2\right)=2430\)
\(\Rightarrow3^x.10=2430\)
\(\Rightarrow3^x=2430:10\)
\(\Rightarrow3^x=243\)
\(\Rightarrow3^x=3^5\)
\(\Rightarrow x=5\)
Vậy \(x=5.\)
c) \(\left(2x-15\right)^5=\left(2x-15\right)^3\)
\(\Rightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\)
\(\Rightarrow\left(2x-15\right)^3.\left[\left(2x-15\right)^2-1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x-15=0\\\left(2x-15\right)^2=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=15\\2x-15=\pm1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=15:2\\2x-15=1\\2x-15=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{15}{2}\\2x=16\\2x=14\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{15}{2}\\x=8\\x=7\end{matrix}\right.\)
Vậy \(x\in\left\{\frac{15}{2};8;7\right\}.\)
Chúc bạn học tốt!
Bạn dùng công thức này mà làm nhé :\(\frac{n}{a\times\left(a+n\right)}=\frac{1}{a}-\frac{1}{a+n}\)
Ví dụ :\(\frac{2}{3\times5}=\frac{1}{3}-\frac{1}{5};\frac{3}{4\times7}=\frac{1}{4}-\frac{1}{7};\frac{5}{6\times11}=\frac{1}{6}-\frac{1}{11}\)
\(\dfrac{3}{4}-\left[\left(-\dfrac{3}{5}\right)-\left(\dfrac{1}{12}+\dfrac{2}{4}\right)\right]\\ =\dfrac{3}{4}-\left[\left(-\dfrac{3}{5}\right)-\left(\dfrac{1}{12}+\dfrac{6}{12}\right)\right]\\ =\dfrac{3}{4}-\left[\left(-\dfrac{3}{5}\right)-\dfrac{7}{12}\right]\\ =\dfrac{3}{4}-\left[\left(-\dfrac{36}{60}\right)-\dfrac{35}{60}\right]\\ =\dfrac{3}{4}-\left(-\dfrac{71}{60}\right)\\ =\dfrac{3}{4}+\dfrac{71}{60}\\ =\dfrac{35}{60}+\dfrac{71}{60}\\ =\dfrac{106}{60}\\ =\dfrac{53}{30}\)
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\(-\dfrac{6}{7}.\dfrac{21}{12}\\ =-\dfrac{126}{84}\\ =-\dfrac{63}{42}\\ =-\dfrac{31}{14}\)
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\(\left(-5\right).\left(-\dfrac{6}{20}\right)\\ =\dfrac{\left(-5\right).\left(-6\right)}{20}\\ =\dfrac{30}{20}\\ =\dfrac{3}{2}\)
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Câu 1:
a) Ta có: 2n+1 là số lẻ∀n
⇒\(\left(-1\right)^{2n+1}=-1\)
Ta có: \(\left(-25\right)\cdot21\cdot\left(-2\right)^2\cdot\left(-\left|-3\right|\right)\cdot\left(-1\right)^{2n+1}\)
\(=-25\cdot21\cdot4\cdot\left(-3\right)\cdot\left(-1\right)\)
\(=75\cdot84\cdot\left(-1\right)\)
\(=-6300\)
b) Ta có: \(\left(-5\right)^3\cdot67\cdot\left(-\left|-2^3\right|\right)\cdot\left(-1\right)^{2n}\)
\(=-125\cdot67\cdot\left(-8\right)\)
\(=1000\cdot67=67000\)
c) Ta có: \(35\cdot18-5\cdot7\cdot28\)
\(=35\cdot18-35\cdot28\)
\(=35\cdot\left(18-28\right)=35\cdot\left(-10\right)=-350\)
d) Ta có: \(24\cdot\left(16-5\right)-16\cdot\left(24-5\right)\)
\(=24\cdot16-24\cdot5-24\cdot16+16\cdot5\)
\(=-24\cdot5+16\cdot5\)
\(=5\cdot\left(-24+16\right)=5\cdot\left(-8\right)=-40\)
e) Ta có: \(29\cdot\left(19-13\right)-19\cdot\left(19-13\right)\)
\(=6\cdot\left(29-19\right)=6\cdot10=60\)
g)Sửa đề: \(31\cdot\left(-18\right)+31\cdot\left(-81\right)-31\)
Ta có: \(31\cdot\left(-18\right)+31\cdot\left(-81\right)-31\)
\(=31\cdot\left(-18-81-1\right)\)
\(=31\cdot\left(-100\right)=-3100\)
h) Ta có: \(\left(-12\right)\cdot47+\left(-12\right)\cdot52+\left(-12\right)\)
\(=-12\cdot\left(47+52+1\right)\)
\(=-12\cdot100=-1200\)
k) Ta có: \(13\cdot\left(23+22\right)-3\cdot\left(17+28\right)\)
\(=13\cdot45-3\cdot45\)
\(=45\cdot\left(13-3\right)=45\cdot10=450\)
m) Ta có: \(-48+48\cdot\left(-78\right)+48\cdot\left(-21\right)\)
\(=48\cdot\left(-1-78-21\right)\)
\(=48\cdot\left(-100\right)=-4800\)
n) Ta có: \(135\cdot\left(171-123\right)-171\cdot\left(135-123\right)\)
\(=135\cdot171-135\cdot123-171\cdot135+171\cdot123\)
\(=123\cdot\left(-135+171\right)=123\cdot36=4428\)
1/3 = 1515/4545
2:2/3 = 3
1 va 1/3 = 1/6 . 8
5/6 = 2 va 1/3-1 va 1/2 ( cau nnay viet de bi sai)
7/12 = 1/3+1/4
1/5 = 1/3 . 3/5
1/2 :1/5 = 2 va 1/2
3/8 = 1/2 -1/8
1/3:1/2 = 2/3
1/3:2 = 1/6