Question

1/Tìm x,biết:

a)x+(x+1)+(x+2)+(x+3)+...+(x+99)+(x+100)=5555

b)1+2+3+4+...+x=820

c)3^(x+1)=9.27

d)x+2x+3x+...+99x+100x=15150

e)(x+1)+(x+2)+(x+3)+...+(x+100)=205550

f)3^x+3^x+1+3^x+2=351

Answer 1

a)x+(x+1)+(x+2)+(x+3)+...+(x+99)+(x+100)=5555

=> 101x +5050 = 5555

=> 101x = 505

=> x = 505 : 101 = 5

Vậy, x = 5

b)1+2+3+4+...+x=820

=> ( x+1) x :2 = 820

=> (x+1)x = 1640

Mà 1640 = 40 . 41

=> x = 40 ( vì {x+1} - x = 1)

Vậy, x = 40

c) 3^x+1 = 9.27=243

=> 3^x+1 = 3⁵

=>x + 1 = 5

=> x = 4

Vậy, x=4

d) x+2x+3x+...+99x+100x=15150

=> [( 100 + 1) x 100 :2 ] x = 15150

=> 5050x = 15150

=> x = 15150:5050 = 3

Vậy, x =3

e)(x+1)+(x+2)+(x+3)+...+(x+100)=205550

=> 100x + 5050 = 205550

=> 100x =  205550 - 5050= 200500

=> x =  200500 : 100 = 2005

Vậy, x = 2005

f)3^x+3^x+1+3^x+2=351

=> 3^x + 3^x . 3 + 3^x x 9 = 351

=> 3^x ( 1+3+9) = 351

=> 3^x  . 13 = 351

=> 3^x  = 351 :13=27 mà 27 = 3³

=> x=3

Vậy, x=3

Answer 2

mình đg cần gấp á

 

Answer 3

a) \(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=5555\)

\(\Rightarrow x+x+1+x+2+x+3+...+x+100=5555\)

\(\Rightarrow101\cdot x+5050=5555\)

\(\Rightarrow101\cdot x=5555-5050\)

\(\Rightarrow101\cdot x=505\)

\(\Rightarrow x=505:101\)

\(\Rightarrow x=5\)

b) \(1+2+3+4+...+x=820\)

\(\Rightarrow\left(x+1\right)\cdot\left[\left(x-1\right):1+1\right]:2=820\)

\(\Rightarrow\left(x+1\right)\cdot\left(x+1-1\right):2=820\)

\(\Rightarrow\left(x+1\right)\cdot x:2=820\)

\(\Rightarrow x\cdot\left(x+1\right)=820\cdot2\)

\(\Rightarrow x\cdot\left(x+1\right)=1640\)

Ta thấy: \(40\cdot41=1640\)

Vậy: \(x=40\)

Answer 4

c) \(3^{x+1}=9\cdot27\)

\(\Rightarrow3^{x+1}=3^2\cdot3^3\)

\(\Rightarrow3^{x+1}=3^5\)

\(\Rightarrow x+1=5\)

\(\Rightarrow x=4\)

d) \(x+2x+3x+...+100x=15150\)

\(\Rightarrow x\cdot\left(1+2+3+4+...+100\right)=15150\)

\(\Rightarrow x\cdot5050=15150\)

\(\Rightarrow x=15150:505\)

\(\Rightarrow x=3\)

e) \(\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=205550\)

\(\Rightarrow x+1+x+2+...+x+100-205550\)

\(\Rightarrow x\cdot100+5050=205550\)

\(\Rightarrow x\cdot100=205550-505\)

\(\Rightarrow x\cdot100=200500\)

\(\Rightarrow x=200500:100\)

\(\Rightarrow x=2005\)

f) \(3^x+3^{x+1}+3^{x+2}=351\)

\(\Rightarrow3^x\cdot\left(1+3^1+3^2\right)=3501\)

\(\Rightarrow3^x\cdot13=351\)

\(\Rightarrow3^x=351:13\)

\(\Rightarrow3^x=27\)

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

\(\Rightarrow x=3\)