Mình gõ câu a bị lỗi nha , thực chất câu a là

a) Tìm các số tự nhiên x, y biết : 2xy + x + 2y = 13

a)Bạn làm nha vì bài này dễ rồi

b)+)Ta có:A=1.2+2.3+3.4+..................+99.100

=>3A=1.2.3+2.3.3+3.4.3+.................+99.100.3

=>3A=1.2.3+2.3.(4-1)+3.4.(5-2)+................+99.100.(101-98)

=>3A=1.2.3-1.2.3+2.3.4-2.3.4+3.4.5-...................-98.99.100+99.100.101

=>3A=99.100.101

=>A=\(\frac{99.100.101}{3}=333300\)

+)Ta lại có:B=1²+2²+3²+..................+99²

=>B=1.1+2.2+3.3+............+99.99

=>B=1.(2-1)+2.(3-1)+3.(4-1)+..........+99.(100-1)

=>B=1.2-1+2.3-2+3.4-3+........................+99.100-99

=>B=(1.2+2.3+3.4+............+99.100)-(1+2+3+..............+99)

Đặt N=1.2+2.3+3.4+....................+99.100

=>3N=1.2.3+2.3.3+3.4.3+.................+99.100.3

=>3N=1.2.3+2.3.(4-1)+3.4.(5-2)+................+99.100.(101-98)

=>3N=1.2.3-1.2.3+2.3.4-2.3.4+3.4.5-...................-98.99.100+99.100.101

=>3N=99.100.101

=>N=\(\frac{99.100.101}{3}=333300\)

Đặt M=1+2+3+..............+99(có 99 số hạng)

=>M=\(\frac{\left(1+99\right).99}{2}=4950\)

+)Ta thấy A-B=333300-(333300-4950)

=>A-B=333300-333300+4950

=>A-B=4950\(⋮\)50

Vậy A-B\(⋮\)50

Chúc bn học tốt

Mk làm câu a cho

2xy+x+2y=13

=>2y.(x+1)+(x+1)=14

=>(2y+1).(x+1)=14

=>14\(⋮\)2y+1

=>2y+1\(\inƯ\left(14\right)=\left\{\pm1;\pm2;\pm7;\pm14\right\}\)

Mà 2y+1 là lẻ

=>2y+1\(\in\left\{\pm1;\pm7\right\}\)

+)Ta có bảng:

Vậy (x,y)\(\in\){(0;6);(3;0)}

Chúc bn học tốt

So sánh : và \(72^{44}-72^{43}\)

Ta có :

       \(72^{45}-72^{44}=72^{44}\left(72-1\right)\)

       \(72^{44}-72^{43}=72^{43}\left(72-1\right)\)

Vì 72⁴⁴ > 72⁴³ => 72⁴⁴ (72-1)  > 72⁴³ (72-1)

                    hay 72⁴⁵ -72⁴⁴ > 72⁴⁴ - 72⁴³ 

Nhanh hộ mọi người😦😦😦😦😦😨

Bài 6 :

a) \(\dfrac{625}{5^n}=5\Rightarrow\dfrac{5^4}{5^n}=5\Rightarrow5^{4-n}=5^1\Rightarrow4-n=1\Rightarrow n=3\)

b) \(\dfrac{\left(-3\right)^n}{27}=-9\Rightarrow\dfrac{\left(-3\right)^n}{\left(-3\right)^3}=\left(-3\right)^2\Rightarrow\left(-3\right)^{n-3}=\left(-3\right)^2\Rightarrow n-3=2\Rightarrow n=5\)

c) \(3^n.2^n=36\Rightarrow\left(2.3\right)^n=6^2\Rightarrow\left(6\right)^n=6^2\Rightarrow n=6\)

d) \(25^{2n}:5^n=125^2\Rightarrow\left(5^2\right)^{2n}:5^n=\left(5^3\right)^2\Rightarrow5^{4n}:5^n=5^6\Rightarrow\Rightarrow5^{3n}=5^6\Rightarrow3n=6\Rightarrow n=3\)

Bài 7 :

a) \(3^x+3^{x+2}=9^{17}+27^{12}\)

\(\Rightarrow3^x\left(1+3^2\right)=\left(3^2\right)^{17}+\left(3^3\right)^{12}\)

\(\Rightarrow10.3^x=3^{34}+3^{36}\)

\(\Rightarrow10.3^x=3^{34}\left(1+3^2\right)=10.3^{34}\)

\(\Rightarrow3^x=3^{34}\Rightarrow x=34\)

b) \(5^{x+1}-5^x=100.25^{29}\Rightarrow5^x\left(5-1\right)=4.5^2.\left(5^2\right)^{29}\)

\(\Rightarrow4.5^x=4.25^{2.29+2}=4.5^{60}\)

\(\Rightarrow5^x=5^{60}\Rightarrow x=60\)

c) Bài C bạn xem lại đề

d) \(\dfrac{3}{2.4^x}+\dfrac{5}{3.4^{x+2}}=\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{10}}\)

\(\Rightarrow\dfrac{3}{2.4^x}-\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{x+2}}-\dfrac{5}{3.4^{10}}=0\)

\(\Rightarrow\dfrac{3}{2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)+\dfrac{5}{3.4^2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)=0\)

\(\Rightarrow\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)\left(\dfrac{3}{2}+\dfrac{5}{3.4^2}\right)=0\)

\(\Rightarrow\dfrac{1}{4^x}-\dfrac{1}{4^8}=0\)

\(\Rightarrow\dfrac{4^8-4^x}{4^{x+8}}=0\Rightarrow4^8-4^x=0\left(4^{x+8}>0\right)\Rightarrow4^x=4^8\Rightarrow x=8\)

5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha

brabla

b) n mũ 2 + 2006 là hợp số

hai câu còn lại ko bt

Hok tốt

^_^

a, \(A=\left(3+3^2+3^3+3^4\right)+\left(3^5+3^6+3^7+3^8\right)+...+\left(3^{97}+3^{98}+3^{99}+3^{100}\right)\)

        \(=120+3^4.\text{​​}\text{​​}\text{​​}\text{​​}\left(3+3^2+3^3+3^4\right)+...+3^{96}.\left(3+3^2+3^3+3^4\right)\)

        \(=120+3^4.110+...+3^{96}.120\)  

         \(=120.\left(1+3^4+...+3^{96}\right)⋮120\)

\(\RightarrowĐPCM\)

Hok Tốt!

# mui #

1a.4,9,16,25,36,49,64,91,110,121,144,169,400,900,1600

b. 8,27,64,125,1000

C1111^2=1234321

2. x=6   ,x=3,x=0, x k thuộc n, x k thuộc n

sao bai 2 ban lamminh ko hieu ?

\(A=3+3^2+....+3^{99}\)

\(3A=3^2+3^3+...+3^{100}\)

\(3A-A=3^2+3^3+...+3^{100}-3-3^2-...-3^{99}\)

\(2A=3^{100}-3\)

\(A=\dfrac{3^{100}-3}{2}\)

\(\Rightarrow2A+3=9^{2x+6}\)

\(\Rightarrow2\cdot\dfrac{3^{100}-3}{2}+3=\left(3^2\right)^{2x+6}\)

\(\Rightarrow3^{100}-3+3=3^{2\left(2x+6\right)}\)

\(\Rightarrow3^{100}=3^{4x+12}\)

\(\Rightarrow4x+12=100\)

\(\Rightarrow4x=88\)

\(\Rightarrow x=22\)

a) \(5.3^x=405\)

\(\Rightarrow3^x=405:5\)

\(\Rightarrow3^x=81=3^4\)

\(\Rightarrow x=4\)

b) \(\left(x-2\right)^5=243\)

\(\Rightarrow\left(x-2\right)^5=3^5\)

\(\Rightarrow x-2=3\)

\(\Rightarrow x=5\)

c) \(2^x+2^{x+4}=272\)

\(\Rightarrow2^x.\left(1+2^4\right)=272\)

\(\Rightarrow2^x.17=272\)

\(\Rightarrow2^x=272:17=16\)

\(\Rightarrow2^x=2^4\)

\(\Rightarrow x=4\)

d) Từ x + 1 đến x + 2 có số số hạng là: (30 - 1) : 1 + 1 = 30 (số)

\(\left(x+1\right)+\left(x+2\right)+...+\left(x+30\right)=795\)

\(\Rightarrow30x+\frac{\left(30+1\right).30}{2}=795\)

\(\Rightarrow30x+465=795\)

\(\Rightarrow30x=330\)

\(\Rightarrow x=330:30\)

\(\Rightarrow x=11\)

a) \(5.3^x=405\)

         \(3^x=\frac{405}{5}=81\)

          \(3^x=3^4\)

Vậy x = 4

b ) \(\left(x-2\right)^5=243\)

      \(\left(x-2\right)^5=3^5\)

\(\Rightarrow x-2=3\)

\(\Rightarrow x=3+2=5\)

     Vậy x = 5

a, 5.3 ^x =405

3^x=405:5

3^x=81

=> x=4

b, (x-2)⁵=243

(x-2)⁵=3⁵

vì 5=5

nên x -2=3

<=> x=3+2

=>x=5

c, 2x  +   2x+4  =  272 

2^x+2^x+2⁴=272

2^x(1+2⁴)=272

2^x.17=272

2^x=272:17

2^x=16

vì 16=2⁴

=>x=4

d, (x+1)+(x+2)+(x+3)+.....+(x+30)=795

(x+x+x+..+x)+(1+2+3+..+30)=795

30x+456=795

30x=795-456

30x=330

x=330:30

x=11

vậy x=11

hc tốt