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\(n^2+4⋮n-1\)
Mà \(n-1⋮n-1\)
\(\Leftrightarrow\hept{\begin{cases}n^2+4⋮n-1\\n^2-n⋮n-1\end{cases}}\)
\(\Leftrightarrow n+4⋮n-1\)
Mà \(n-1⋮n-1\)
\(\Leftrightarrow5⋮n-1\)
\(\Leftrightarrow n-1\inƯ\left(5\right)\)
\(\Leftrightarrow\orbr{\begin{cases}n-1=1\\n-1=5\end{cases}}\) \(\Leftrightarrow\orbr{\begin{cases}n=0\\n=6\end{cases}}\)
5 + n2 - 2n \(⋮\)n - 2
=> 5 + n . n - 2 . n \(⋮\)n - 2
=> 5 + n . ( n - 2 ) \(⋮\)n - 2
=> 5 \(⋮\)n - 2 vì n . ( n - 2 ) đã chia hết cho n - 2
=> n - 2 \(\in\)Ư ( 5 ) = { 1 ; -1 ; 5 ; -5 }
Với n - 2 = 1 => n = 3
Với n - 2 = -1 => n = 1
Với n - 2 = 5 => n = 7
Với n - 2 = -5 => n = -3
Vậy : n \(\in\){ 3 ; 1 ; 7 ; -3 }
Để \(5+n^2-2n⋮n-2\)
\(\Leftrightarrow5+n.\left(n-2\right)⋮n-2\)
\(\Leftrightarrow5⋮n-2\)
\(\Leftrightarrow n-2\inƯ\left(5\right)\)
\(\Leftrightarrow n-2\in\left\{1;-1;5;-5\right\}\)
\(\Leftrightarrow n\in\left\{3;1;7;-3\right\}\)
Chúc bạn học tốt !!!!
a)Ta có: \(5^{36}=5^{3.12}=\left(5^3\right)^{12}=125^{12}\)
\(11^{24}=11^{2.12}=\left(11^2\right)^{12}=121^{12}\)
Vì \(125>121\Rightarrow125^{12}>121^{12}\)
\(\Rightarrow5^{36}>11^{24}\)
b) Ta có: \(625^5=\left(5^4\right)^5=5^{20}\)
\(125^7=\left(5^3\right)^7=5^{21}\)
Vì \(20< 21\Rightarrow5^{20}< 5^{21}\)
\(\Rightarrow625^5< 125^7\)
c) Ta có: \(3^{2n}=\left(3^2\right)^n=9^n\)
\(2^{3n}=\left(2^3\right)^n=8^n\)
Vì \(9>8\Rightarrow9^n>8^n\)( do \(n>0\))
\(\Rightarrow3^{2n}>2^{3n}\)
d)Ta có: \(5^{23}=5.5^{22}< 6.5^{22}\)
\(\Rightarrow5^{23}< 6.5^{22}\)
a. 5^36=(5^3)^12
=125^12
11^24=(11^2)^12
= 121^12
Vì 125^12>121^12 nên 5^36>11^24
b. Ta có: 625^5 =(5^4)^5
= 5^20
125^7=(5^3)^7
= 5^21
Vì 5^20<5^21 nên 625^5<125^7
\(\Leftrightarrow n-2\in\left\{1;-1;5;-5\right\}\)
hay \(n\in\left\{3;1;7;-3\right\}\)
A=(2+22)+(23+24)+....+(21995+21996)(NHÓM SỐ BẠN NHÉ)
A=6+6.22+....+6.21994
A=6.(1+22+...+21994) CHIA HẾT CHO 6
VẬY...( BẠN LÀM RỒI 100%)
n2+3⋮n+1n2+3⋮n+1
⇒n2+n+3−n⋮n+1⇒n2+n+3−n⋮n+1
⇒n(n+1)−n+3⋮n+1⇒n(n+1)−n+3⋮n+1
Vì n(n+1)⋮n+1n(n+1)⋮n+1
nên −n+3⋮n+1−n+3⋮n+1
⇒−n−1+4⋮n+1⇒−n−1+4⋮n+1
⇒−(n+1)+4⋮n+1⇒−(n+1)+4⋮n+1
Vì −(n+1)⋮n+1−(n+1)⋮n+1
nên 4⋮n+14⋮n+1
⇒n+1∈Ư(4)={±1;±2;±4}⇒n+1∈Ư(4)={±1;±2;±4}
⇒n∈{0;−2;1;−3;3;−5}⇒n∈{0;−2;1;−3;3;−5}
Nếu bạn ko hiểu thì mik gửi ảnh cho:
Ta có: n3+n2+1⋮n+1" role="presentation" style="box-sizing: inherit; -webkit-tap-highlight-color: transparent; font-style: normal; font-weight: normal; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">n3+n2+1⋮n+1n3+n2+1⋮n+1
⇔n2(n+1)+1⋮n+1" role="presentation" style="box-sizing: inherit; -webkit-tap-highlight-color: transparent; font-style: normal; font-weight: normal; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">⇔n2(n+1)+1⋮n+1⇔n2(n+1)+1⋮n+1
mà n2⋅(n+1)⋮n+1" role="presentation" style="box-sizing: inherit; -webkit-tap-highlight-color: transparent; font-style: normal; font-weight: normal; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">n2⋅(n+1)⋮n+1n2⋅(n+1)⋮n+1
nên 1⋮n+1" role="presentation" style="box-sizing: inherit; -webkit-tap-highlight-color: transparent; font-style: normal; font-weight: normal; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">1⋮n+11⋮n+1
⇔n+1∈Ư(1)" role="presentation" style="box-sizing: inherit; -webkit-tap-highlight-color: transparent; font-style: normal; font-weight: normal; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">⇔n+1∈Ư(1)⇔n+1∈Ư(1)
⇔n+1∈{1;−1}" role="presentation" style="box-sizing: inherit; -webkit-tap-highlight-color: transparent; font-style: normal; font-weight: normal; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">⇔n+1∈{1;−1}⇔n+1∈{1;−1}
hay n∈{0;−2}" role="presentation" style="box-sizing: inherit; -webkit-tap-highlight-color: transparent; font-style: normal; font-weight: normal; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">n∈{0;−2}n∈{0;−2}
Vậy: Để n3+n2+1⋮n+1" role="presentation" style="box-sizing: inherit; -webkit-tap-highlight-color: transparent; font-style: normal; font-weight: normal; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">n3+n2+1⋮n+1n3+n2+1⋮n+1 thì n∈{0;−2}" role="presentation" style="box-sizing: inherit; -webkit-tap-highlight-color: transparent; font-style: normal; font-weight: normal; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-size: 18.08px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">n∈{0;−2}
CHÚC BẠN HỌC TỐT!