Giúp em giải:
X-2120=3/4×(21210-X+2121)
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\(\frac{210}{209}>1;\frac{3}{2}>1;\frac{28}{28}=1;\frac{7}{8}<1;\frac{5}{6}<1;\frac{2120}{2121}<1\)
ta co ta co
\(\frac{210}{209}-\frac{1}{209}=1\) \(\frac{7}{8}+\frac{1}{8}=1\)
\(\frac{3}{2}-\frac{1}{2}=1\) \(\frac{5}{6}+\frac{1}{6}=1\)
vi \(\frac{1}{209}<\frac{1}{2}\) nen \(\frac{210}{209}<\frac{3}{2}\) \(\frac{2120}{2121}+\frac{1}{2121}=1\)
vi \(\frac{1}{6}>\frac{1}{8}>\frac{1}{2121}nen\frac{5}{6}<\frac{7}{8}<\frac{2120}{2121}\)
--->\(\frac{5}{6}<\frac{7}{8}<\frac{2120}{2121}<\frac{28}{28}<\frac{210}{209}<\frac{3}{2}\)
\(\frac{13}{21}\times27225\div20449\times0,100\)
=\(16853,57143\div2044,9\)
=\(8,2417\)
a, 6100 - 1 = (6 . 6 . 6 ..... 6) - 1 = [(...6) . (...6) . (...6) ..... (...6)] - 1 = (...6) - 1 = ...5 \(⋮\) 5
b, 2120 - 1110 = (21 . 21 . 21 . 21 . 21..... 21) - (11 . 11 . 11 . 11 ..... 11) = [(...1) . (...1) . (...1) . (...1).....(...1)] - [(...1) . (...1) . (...1) . (...1).....(...1)] = (...1) - (...1) = ....0 \(⋮\) 2; \(⋮\) 5
\(0^{2020}\cdot1^{2021}\cdot....\cdot21^{2120}=0\cdot1^{2021}\cdot...\cdot21^{2120}=0\)
a) Dễ thấy P = 102120 + 2120
= 102120 + 212.10
= 10(102119 + 212)
=> P \(⋮10\)
Lại có P = 102120 + 2120
= 10(102119 + 212)
= 10.(1000...00 + 212)
2119 số 0
= 10.1000...0212
2116 số 0
Tổng các chữ số của số S = 1000...0212 (2116 chữ số 0)
là 1 + 0 + 0 + 0 +.... + 0 + 2 + 1 + 2 (2116 hạng tử 0)
= 1 + 2 + 1 + 2 = 6 \(⋮3\)
=> S \(⋮3\Rightarrow P=10S⋮3\)
mà \(\left\{{}\begin{matrix}P⋮10\\P⋮3\\\left(10,3\right)=1\end{matrix}\right.\Rightarrow P⋮10.3\Rightarrow P⋮30\)
Gọi (a,b) = d \(\left(d\inℕ^∗;d\ne1\right)\)
=> \(\left\{{}\begin{matrix}a⋮d\\b⋮d\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2n+3⋮d\\5n+2⋮d\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}5.(2n+3)⋮d\\2.(5n+2)⋮d\end{matrix}\right.\)
=> \(\left\{{}\begin{matrix}10n+15⋮d\left(1\right)\\10n+4⋮d\left(2\right)\end{matrix}\right.\)
Lấy (1) trừ (2) ta được
(10n + 15) - (10n + 4) \(⋮d\)
<=> 11 \(⋮d\)
\(\Leftrightarrow d\in\left\{1;11\right\}\) mà d \(\ne1\)
<=> d = 11
Vậy (a;b) = 11
X thuộc Z
\(x-2120=\frac{3}{4}\left(21210-x+2121\right)\)
\(x-2120=-\frac{3x}{4}+\frac{69993}{4}\)
\(x=\frac{-3x+69993}{4}+2120\)
\(x\cdot \:4=\frac{-3x+69993}{4}\cdot \:4+2120\cdot \:4\)
\(4x=-3x+69993+8480\)
\(4x=-3x+78473\)
\(4x+3x=-3x+78473+3x\)
\(7x=78473\)
\(x=78473:7\)
\(x=\frac{78473}{7}\)