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5, 31+1240++1829=3100
6. -19+836+1829=2646
7. 54.43-32.35=2322-1120=1202
8 2018(31+16+50)=2018.97=195746
9. 16(34-21+55)=16.68=1088
10. 63(29-31-98)=63.(-100)=-6300
a)\(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\Leftrightarrow\left(x-1\right)^{x+2}\left[\left(x-1\right)^2-1\right]=0\Leftrightarrow x\left(x-1\right)^{x+2}\left(x-2\right)=0\)
Do đó \(x\in\left\{0;1;2\right\}\)
b)
\(\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{3}{8}\cdot...\cdot\frac{31}{64}=2^x\Leftrightarrow\frac{1\cdot2\cdot3\cdot...\cdot31}{4\cdot6\cdot8\cdot...\cdot64}=2^x\Leftrightarrow\frac{31!}{\left(2\cdot2\right)\cdot\left(2\cdot3\right)\cdot\left(2\cdot4\right)\cdot...\cdot\left(2\cdot31\right)\cdot64}=2^x\)
\(\frac{31!}{2^{30}\cdot31!\cdot2^6}=2^x\Leftrightarrow\frac{1}{2^{36}}=2^x\Leftrightarrow2^{-36}=2^x\Rightarrow x=-36\)
91 x 157 - 29 x 91 - 91 x 28
=9100
127 x 63 + 19 x 127 - 82 x 26
=8282
2 x 9 x 41 + 36 + 3 x 57 x 6
=1800
29 x 17 + 31 x 29 + 48 x 93 - 48 x 22
=4800
1125 - 25 x 30 + 0,06 : 0,2
=375.3
Bn k cho mk nha!
91 x 157 - 29 x 91 - 91 x 28
= 19 (157 - 29 - 28)
=19 * 100
=1900
127 x 63 + 19 x 127 - 82 x 26
= 127 (63 + 19) - 82 * 26
= 127 * 82 - 82 * 26
= 82 (127 - 26)
= 82 * 101
= 8282
2 x 9 x 41 + 36 + 3 x 57 x 6
= 738 + 36 + 1026
= 1800
29 x 17 + 31 x 29 + 48 x 93 - 48 x 22
= 29 (17 + 31) + 48 (93 - 22)
= 29 * 48 + 48 * 71
= 48 (29 + 71)
= 48 * 100
= 4800
1125 - 25 x 30 + 0,06 : 0,2
= 1125 - 750 + 0,3
= 375 + 0,3
= 375,3
\(\frac{1.2.3.4....30.31}{2.2.2.3.2.3.....2.32}=\frac{2.3.4....30.31}{2^{31}\left(2.3...31\right).32}=\frac{1}{2^{31}.2^5}=\frac{1}{2^{36}}=2^{-36}\)
Vậy x=-36
ta có \(\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{3}{8}.....\frac{30}{62}\cdot\frac{31}{64}=2^x\)
=>\(\frac{1.2.3.4....31}{2\cdot2\cdot2\cdot3\cdot2\cdot3.....\cdot2\cdot3\cdot2}=\frac{2\cdot3\cdot4...30.31}{2^{31}\left(2\cdot3\cdot4...31\right)32}=\frac{1}{2^{31}\cdot2^5}=\frac{1}{2^{36}}=2^{-36}\)
\(=>x=-36\)
Tính từng phép tính trong ngoặc ta được :
\(A= \frac{3}{4}. \frac{8}{9} . ....\frac{899}{900}\)
\(A=\frac{1.3}{2.2} .\frac{2.4}{3.3}.... \frac{29.31}{30.30}\)
Gộp các thừa số với sau được
\(A= \frac{(1.2.3.4....29)(3.4.5.6...31)}{(2.3.4...30)(2.3.4..30)}\)
\(A= \frac{31}{30.2} = \frac{31}{60}\)
\(a,\frac{x+1}{65}+\frac{x+2}{64}=\frac{x+3}{63}+\frac{x+4}{62}\)
\(\Rightarrow\left[\frac{x+1}{65}+1\right]+\left[\frac{x+2}{64}+1\right]=\left[\frac{x+3}{63}+1\right]+\left[\frac{x+4}{62}+1\right]\)
\(\Rightarrow\frac{x+1+65}{65}+\frac{x+2+64}{64}=\frac{x+3+63}{63}+\frac{x+4+62}{62}\)
\(\Rightarrow\frac{x+66}{65}+\frac{x+66}{64}=\frac{x+66}{63}+\frac{x+66}{62}\)
\(\Rightarrow\frac{x+66}{65}+\frac{x+66}{64}=\frac{x+66}{63}+\frac{x+66}{62}=0\)
\(\Rightarrow\left[x+66\right]\left[\frac{1}{65}+\frac{1}{64}-\frac{1}{63}+\frac{1}{62}\right]=0\)
Mà \(\frac{1}{65}+\frac{1}{64}-\frac{1}{63}+\frac{1}{62}\ne0\)
\(\Rightarrow x+66=0\)
\(\Rightarrow x=0-66=-66\)
Auto làm nốt câu b
a, Cộng cả 2 vế với 2
Ta có \(\frac{x+1}{64}+\frac{x+2}{63}+2=\frac{x+3}{62}+\frac{x+4}{61}+2\)
\(\left(\frac{x+1}{64}+\frac{64}{64}\right)+\left(\frac{x+2}{63}+\frac{63}{63}\right)=\left(\frac{x+3}{62}+\frac{62}{62}\right)+\left(\frac{x+4}{61}+\frac{61}{61}\right)\)
=> \(\frac{x+65}{64}+\frac{x+65}{63}=\frac{x+65}{62}+\frac{x+65}{61}\)\(\)
=> \(\frac{x+65}{64}+\frac{x+65}{63}-\frac{x+65}{62}-\frac{x+65}{61}=0\)
=> \(\left(x+65\right)\left(\frac{1}{64}+\frac{1}{63}-\frac{1}{62}-\frac{1}{61}\right)=0\)
Do \(\frac{1}{64}+\frac{1}{63}-\frac{1}{62}-\frac{1}{61}\ne0\)=> \(x+65=0\)
=> \(x=-65\)
b , Lm tương tự như Câu a
Chúc bn hok tốt
\(\frac{x^{63}+x^{62}+...+x^2+x+1}{x^{31}+x^{30}+x^{29}+...+x^2+x+1}\)
hay \(\frac{1+x+x^2+...+x^{63}}{1+x+x^2+...+x^{31}}=\frac{x^{32}+x^{33}+x^{34}+...+x^{63}}{1}=x^{32}+x^{33}+x^{34}+...+x^{63}\)