CMR vs mọi n thì :
a, ( n2 + 3n -1 ) ( n + 2 ) - n3 + 5 ⋮ 5
b, ( 6n + 1 ) ( n + 5 ) - ( 3n + 5 ) ( 2n - 1 ) ⋮ 2
c, xn ( x = 1 ) + xn ( y - 1 ) ⋮ 13 ( x,y ∈ N, x + y ⋮ 13 )
d, ( 2x2 + x ) ( 2y2 - y ) - xy ( 4 xy - 1 ) ⋮ 2
e, ( xy - 1 ) ( x2003 + y2003 ) - ( xy + 1 ) ( x2003 - y2003 )
Bài 1 :
a) (3xn + 1 - 2xn) 4x2
b) 2(x2n + 2xnyn +y2n) -yn(4xn +2yn)
c) (x2n + xnyn+y2n)(xn-yn)(x3n + y3n)
d)4n+1-3.4n
a)2x^2+3.(x-1).(x+1)-5x.(x+1)
b) (8-5x).(x+2)+4.(x-2).(x+1)+2.(x-2).(x+2)+10
c) 4.(x-1).(x+5)-(x+2).(x+5)-3.(x-1).(x+2)
d) (x^2n+x^n y^n +y^2n).(x^n-y^n).(x^3n+y^3n)
GIÚP MÌNH VỚI Ạ
Tìm n thuộc N, để các phân số sau có giá trị là số tự nhiên
a) 3n + 5/ n+1
b) n+13/ n+1
c) 3n +15/ n+1
d) 2n+13/ n-1
e) 3n + 5/ n-2
f) 6n +5/2n+1
a, \(\frac{3n+5}{n+1}=\frac{3\left(n+1\right)+2}{n+1}=\frac{2}{n+1}\)
\(\Rightarrow n+1\in2=\left\{\pm1;\pm2\right\}\)
| n + 1 | 1 | -1 | 2 | -2 |
| n | 0 | -2 | 1 | -3 |
b, \(\frac{n+13}{n+1}=\frac{n+1+12}{n+1}=\frac{12}{n+1}\)
\(\Rightarrow n+1\inƯ\left(12\right)=\left\{\pm1;\pm2;\pm3;\pm4;\pm6;\pm12\right\}\)
| n + 1 | 1 | -1 | 2 | -2 | 3 | -3 | 4 | -4 | 6 | -6 | 12 | -12 |
| n | 0 | -2 | 1 | -3 | 2 | -4 | 3 | -5 | 5 | -7 | 11 | -13 |
c, \(\frac{3n+15}{n+1}=\frac{3\left(n+1\right)+12}{n+1}=\frac{12}{n+1}\)
\(\Rightarrow n+1\inƯ\left(12\right)=\left\{\pm1;\pm2;\pm3;\pm4;\pm6;\pm12\right\}\)
| n + 1 | 1 | -1 | 2 | -2 | 3 | -3 | 4 | -4 | 6 | -6 | 12 | -12 |
| n | 0 | -2 | 1 | -3 | 2 | -4 | 3 | -5 | 5 | -7 | 11 | -13 |
Bài 1: tìm x; y ∈ Z, biết:
a) (x+2).(x-3)=5
b) (x+1).(xy-1)=3
c) (x-3).(2y+1)=7
Bài 2: tìm n∈Z sao cho;
a) n+5⋮n-2
b) 2n +1 ⋮n-5
c) n2+3n -13 ⋮n+3
d) n2 +3 ⋮n-1
2)
a. \(n+5⋮n-2\Rightarrow n-2+7⋮n-2\)
\(\Rightarrow7⋮n-2\Rightarrow n-2\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)
\(\Rightarrow n\in\left\{-5;1;3;9\right\}\)
b. \(2n+1⋮n-5\Rightarrow2n-10+11⋮n-5\)
\(\Rightarrow11⋮n-5\Rightarrow n-5\inƯ\left(11\right)=\left\{\pm1;\pm7\right\}\)
\(\Rightarrow n\in\left\{-6;4;6;16\right\}\)
c. \(n^2+3n-13⋮n+3\)
\(\Rightarrow n.n+3n-13⋮n+3\)
\(\Rightarrow n.\left(n+3\right)-13⋮n+3\)
\(\Rightarrow-13⋮n+3\Rightarrow n+3\inƯ\left(-13\right)=\left\{\pm1;\pm13\right\}\)
\(\Rightarrow n\in\left\{-16;-4;-2;10\right\}\)
d. \(n^2+3⋮n-1\Rightarrow n^2-n+n+3⋮n-1\)
\(\Rightarrow n.\left(n-1\right)+\left(n-1\right)+4⋮n-1\)
\(\Rightarrow4⋮n-1\Rightarrow n-1\inƯ\left(4\right)=\left\{\pm1;\pm2;\pm4\right\}\)
\(\Rightarrow n\in\left\{-3;-1;0;2;3;5\right\}\)
Câu 1:
a: \(\Leftrightarrow x^2-3x+2x-6=5\)
\(\Leftrightarrow x^2-x-11=0\)
hay \(x\in\left\{\dfrac{1+3\sqrt{5}}{2};\dfrac{1-3\sqrt{5}}{2}\right\}\)
b: \(\Leftrightarrow\left(x+1;xy-1\right)\in\left\{\left(1;3\right);\left(3;1\right);\left(-1;-3\right);\left(-3;-1\right)\right\}\)
\(\Leftrightarrow\left(x,xy\right)\in\left\{\left(0;4\right);\left(2;2\right);\left(-2;-2\right);\left(-4;0\right)\right\}\)
\(\Leftrightarrow\left(x,y\right)\in\left\{\left(2;1\right);\left(-2;1\right);\left(-4;0\right)\right\}\)
c: \(\Leftrightarrow\left(x-3;2y+1\right)\in\left\{\left(1;7\right);\left(7;1\right);\left(-1;-7\right);\left(-7;-1\right)\right\}\)
hay \(\left(x,y\right)\in\left\{\left(4;3\right);\left(10;0\right);\left(2;-4\right);\left(-4;-1\right)\right\}\)
a) 2x^2 +3 × ( x - 1)×(x+1)-5x × (x+1)
b) (8-5x)×(x+2)+4× (x-2) × (x +1)+2 × ( x -2)×( x+2)+10
c) 4 × ( x-1) × ( x-5)-( x-2)×( x+5)-3× ( x-1)×( x+2)
d) (x2n + xn yn + y2n)×( xn - yn ) × ( x3n + y3n)
Bài 1: Tìm x , biết :
a) ( x -1).(x-2)=0
b) (x-2).(x^2+1)=0
c) (x+`1).(x^2-4)=0
Bài 2: Tìm x,y \(\inℤ\), biết :
a) xy=-7
b) (2x-3) . (2y+3)=5
c) (x-1) .(y-13)=11
d) (2x-7).(y-5)=17
Bài 3: Tìm số nguyên n sao cho:
a) (3n+2)\(⋮\)(n-1)
b) (3n+24) \(⋮\)(n-4)
c) (n^2+5) \(⋮\)(n+1)
Giúp mình vs mn ơi!
Bài 1: Tìm x , biết :
a) ( x -1).(x-2)=0
<x-1=0
|
<x=0+1=1
-<x-2=0
-<x=0+2=2
Vậy x E {1;2}
b) (x-2).(x^2+1)=0
[<x-2=0
[<x=0+2=2
[>x2+1=0
x2=0-1
x2=1.(-1)
c) (x+`1).(x^2-4)=0
. Bài 1:Tìm x
a; x.(x-4)+x-4=0
b; x.(x-4)=2x-8
c; (2x+3).(x-1)+(2x-3).(1-x)=0
d; (x+1).(6x^2+2x)+(x-1).(6x^2+2x)=0
. Bài 2:Tính giá trị biểu thức
a; A=x.(2y-z)-2y.(z-2y) với x=2,y=1/2,z= -1
b; B=x.(y-x)+y.(x-y) với x=13,y=3
c; C=x.(x+y)-5x-5y với x=33/5,y=12/5
. Bài 3
a; CMR: n^2.(n+1)+2n.(n+1) chia hết cho 6 với mọi n thuộc Z
b; CMR: 24^n+1 - 24^n chia hết cho 23 với mọi n thuộc N
c; CMR: (2^n-1)^2 - 2^n+1 chia hết cho 8 với mọi n thuộc Z
. Bài 4: CMR: m^3 - m chia hết cho 6 với mọi m thuộc Z
bn ... ơi...mik ...bỏ...cuộc ...hu...hu
. Huhu T^T mong sẽ có ai đó giúp mình "((
tìm x thuộc N
a)n+1/n-1
b)7/n-1
c)2n+8/5-n/5
d)3n+5/n+1
e)2n+13/n-1
h)3n+15/n+1
