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b) Ta có: M = 3n + 2 + 2n + 3 + 3n + 2n + 1 = 3n . 32 + 3n + 2n . 23 + 2n . 2 = 3n . (32 + 1) + 2n . (23 + 2) = 3n . 10 + 2n . 10 = (3n + 2n) . 10 \(⋮\) 10.
Vậy...
a) -105 - 5.x = (-5)^2
=>-105 - 5.x = 25
=> 5.x = -105 - 25
=> 5.x = -130
=> x = -130: 5
=> x = -26
c) 400 -4.|5-x| = (-6)^2
=>400- 4.|5-x| = 36
=> 4.|5-x| = 400-36
=> 4.|5-x| = 364
=> |5-x| = 364:4
=> |5-x| = 91
=> \(\left[\begin{matrix}5-x=91\\5-x=-91\end{matrix}\right.\)
=> \(\left[\begin{matrix}x=5-91\\x=5-\left(-91\right)\end{matrix}\right.\)
=> \(\left[\begin{matrix}x=-86\\x=96\end{matrix}\right.\)
\(3,1+5^2+5^4+...+5^{26}\)
\(=\left(1+5^2\right)+\left(5^4+5^6\right)+...+\left(5^{24}+5^{26}\right)\)
\(=\left(1+5^2\right)+5^4\left(1+5^2\right)+...+5^{24}\left(1+5^2\right)\)
\(=26+5^4.26+...+5^{24}.26\)
\(=26\left(5^4+...+5^{24}\right)\)
Vì \(26⋮26\)
\(\Rightarrow26\left(5^4+...+5^{24}\right)⋮26\)
\(\Rightarrow1+5^2+5^4+...+5^{26}⋮26\)
\(4,1+2^2+2^4+...+2^{100}\)
\(=\left(1+2^2+2^4\right)+...+\left(2^{98}+2^{99}+2^{100}\right)\)
\(=\left(1+2^2+2^4\right)+....+2^{98}\left(1+2^2+2^4\right)\)
\(=21+2^6.21...+2^{98}.21\)
\(=21\left(2^6+...+2^{98}\right)\)
Có : \(21\left(2^6+...+2^{98}\right)⋮21\)
\(\Rightarrow1+2^2+2^4+...+2^{100}⋮21\)
1) 2x- 15= 17
=> 2x = 17+ 15
=> 2x = 32
Mà 32= 25
=> 2x= 25
=> x=5
Vậy x=5
2) x10= x
=> \(\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
3) Câu 3 bạn ghi thế thì chịu rồi!
làm cho câu khó nhất:
3) 2.3x = 10.312 + 8.33.4
2.3x = 18.312 = 2.312+2=2.314
x = 14
1) \(1+2+3...............+n=4950\)
\(\Leftrightarrow\dfrac{n\left(n+1\right)}{2}=4950\)
\(\Leftrightarrow n\left(n+1\right)=4950.2\)
\(\Leftrightarrow n\left(n+1\right)=9900\)
\(\Leftrightarrow n\left(n+1\right)=99.100\)
\(\Leftrightarrow n=99\left(tm\right)\)
Vậy ................
1)
1 + 2 + 3 + ... + n = 4950
(n + 1) . n : 2 = 4950
(n + 1) . n = 9900
(n + 1) . n = 100 . 99
Vậy n = 99