7 x 46 + 7 x 54
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[(46-32)^2-(54-42)^2]*36-1872
=(14^2-12^2)*36-1872
=(196-144).36-1872
=52.36-1872
=1872-1872
=0
(x-7)^7=(x-7)^8
=>(x-7)^7-(x-7)^8=0
=>(x-7)^7.1-(x-7)^7.(x-7)=0
=>(x-7)^7.[1-(x-7)]=0
\(\Rightarrow\orbr{\begin{cases}x-7=0\\1-\left(x-7\right)=0\end{cases}\Rightarrow\orbr{\begin{cases}x=7;-7\\x=0\end{cases}}}\)
Vậy x={7;-7;0}
1+2^3+3^3-4^2.x=20
=>36-4^2.x=20
=>4^2.x=16=4^2
=>2.x=2
=>x=1
Giải phương trình:
a) x+1 /9 + x+2 /8 = x+3 /7 + x+4 /6
b) x+43 /57 + x+46 /54 = x+49 /51 + x+52 /48
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\frac{x+1}{9}+\frac{x+2}{8}=\frac{x+3}{7}+\frac{x+4}{6}\)
\(\Rightarrow\left(\frac{x+1}{9}+1\right)+\left(\frac{x+2}{8}+2\right)=\left(\frac{x+3}{7}+1\right)+\left(\frac{x+4}{6}+1\right)\)
\(\Rightarrow\frac{x+10}{9}+\frac{x+10}{8}-\frac{x+10}{7}-\frac{x+10}{6}=0\)
\(\Rightarrow\left(x+10\right)\left(\frac{1}{9}+\frac{1}{8}-\frac{1}{7}-\frac{1}{6}\right)=0\)
Mà \(\frac{1}{9}+\frac{1}{8}-\frac{1}{7}-\frac{1}{6}\ne0\)
\(\Rightarrow x+10=0\)
\(\Rightarrow x=-10\)
Vậy x = -10
b) \(\frac{x+43}{57}+\frac{x+46}{54}=\frac{x+49}{51}+\frac{x+52}{48}\)
\(\Rightarrow\left(\frac{x+43}{57}+1\right)+\left(\frac{x+46}{54}+1\right)=\left(\frac{x+49}{51}+1\right)+\left(\frac{x+52}{48}+1\right)\)
\(\Rightarrow\frac{x+100}{57}+\frac{x+100}{54}=\frac{x+100}{51}+\frac{x+100}{48}\)
\(\Rightarrow\frac{x+100}{57}+\frac{x+100}{54}-\frac{x+100}{51}-\frac{x+100}{48}=0\)
\(\Rightarrow\left(x+100\right)\left(\frac{1}{57}+\frac{1}{54}-\frac{1}{51}-\frac{1}{48}\right)=0\)
Mà \(\frac{1}{57}+\frac{1}{54}-\frac{1}{51}-\frac{1}{48}\ne0\)
\(\Rightarrow x+100=0\)
\(\Rightarrow x=-100\)
Vậy x = -100
a.\(\frac{x+1}{9}+\frac{x+2}{8}=\frac{x+3}{7}+\frac{x+4}{6}\)
=>\(\frac{x+1}{9}+1+\frac{x+2}{8}+1=\frac{x+3}{7}+1+\frac{x+4}{6}+1\)
<=> \(\frac{x+1+9}{9}+\frac{x+2+8}{8}=\frac{x+3+7}{7}+\frac{x+4+6}{6}\)
<=>\(\frac{x+10}{9}+\frac{x+10}{8}=\frac{x+10}{7}+\frac{x+10}{6}\)
<=> \(\frac{x+10}{9}+\frac{x+10}{8}-\frac{x+10}{7}-\frac{x+10}{6}=0\)
<=> \(\left(x+10\right)\left(\frac{1}{9}+\frac{1}{8}-\frac{1}{7}-\frac{1}{6}\right)=0\)
<=> x+10=0
<=> x=-10
Vậy tập nghiệm của phương trình trên là S=\(\left\{-10\right\}\)
b. \(\frac{x+43}{57}+\frac{x+46}{54}=\frac{x+49}{51}+\frac{x+52}{48}\)
=> \(\frac{x+43}{57}+1+\frac{x+46}{54}+1=\frac{x+49}{51}+1+\frac{x+52}{48}+1\)<=>\(\frac{x+43+57}{57}+\frac{x+46+54}{54}=\frac{x+49+51}{51}+\frac{x+52+48}{48}\)
<=>\(\frac{x+100}{57}+\frac{x+100}{54}=\frac{x+100}{51}+\frac{x+100}{48}\)
<=>\(\frac{x+100}{57}+\frac{x+100}{54}-\frac{x+100}{51}-\frac{x+100}{48}=0\)
<=>(x+100)\(\left(\frac{1}{57}+\frac{1}{54}-\frac{1}{51}-\frac{1}{48}\right)\)=0
<=>x+100=0
<=>x= -100
Vậy tập nghiệm của phương trình trên là S=\(\left\{-100\right\}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(3,54\times73+0,46\times25+3,54\times26+0,46\times75+3,54\)
\(=3,54\times\left(73+26+1\right)+0,46\times\left(25+75\right)\)
\(=3,54\times100+0,46\times100\)
\(=354+46=400\)
![](https://rs.olm.vn/images/avt/0.png?1311)
[54.(46+49)]-[46.(54-49)]
=[54.46+54.49]-[54.46-46.49]
=54.46+54.49-54.46+46.49
=54.46-54.46+54.49+46.49
=54.49+46.49
=49.(54+46)
=49.100
=4900
Chúc bn học tốt
\(54\times\left(46+49\right)-46\times\left(54-49\right)\)
\(=54\times46+54\times49-46\times54+46\times49\)
\(=\left(54\times46-46\times54\right)+49\times\left(54+46\right)\)
\(=49\times100\)
\(=4900\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) (44 x 52 x 60) : (11 x 13 x 15)
= 44 x 52 x 60 : 11 : 13 : 15
= (44 : 11) x (52 : 13) x (60 : 15)
= 4 x 4 x 4
= 64
b) 2016 x 20152015 - 2015 x 20162016
= 2016 x (20150000 + 2015) - 2015 x (20160000 + 2016)
= 2016 x (2015 x 10000 + 2015) - 2015 x (2016 x 10000 + 2016)
= 2016 x [2015 x (10000 + 1)] - 2015 x [2016 x (10000 + 1)]
= 2016 x 2015 x 10001 - 2015 x 2016 x 10001
= 0
c) 46 x 37 + 46 x 63 + 54 x 267 - 54 x 167
= 46 x (37 + 63) + 54 x (267 - 167)
= 46 x 100 + 54 x 100
= 100 x (46 + 54)
= 100 x 100
= 10000
![](https://rs.olm.vn/images/avt/0.png?1311)
= 700 nha
=7x(54+46) =700