Question

Tìm x:

a) (x+1) + (x+2) +....+ (x+100) = 5750

b) Cho C = 2 + 2^2 + 2^3 + ...+ 2^100

Tìm x để 2^2x-1 - 2 = C

c) (x^2 + 4) chia hết cho (x+2)            (x thuộc N)

e) 2^3 .x + 5^2.x = 2 (5^2 + 2^3) - 33                 (x thuộc N)

f) (3x - 4)^10 - 3= 1021                    (x thuộc N)

g) (4x - 3)^4 = (4x - 3)^2

h) 2^x+2 . 3^x+1 . 5^x = 10800

Answer 1

(x+1) + (x+2) + ... + (x+100) = 5750

(x+x+...+x) + (1+2+..+100) = 5750

100x + (101 x 100 : 2 ) = 5750

100x + 5050 = 5750

=> 100x = 5750 - 5050 

100 x = 700

=> x = 700 : 100

=> x = 7              

Answer 2

\(a.\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=5750\)

\(\left(x+x+x+...+x\right)+\left(1+2+3+4+...+100\right)=5750\)

\(100x+\left(1+2+3+4+...+100\right)=5750\)

\(100x+5050=5750\)

\(100x=5750-5050\)

\(100x=700\)

\(x=700:100\)

\(x=7\)

Answer 3

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

\(2C=2.\left(2+2^2+2^3+2^4+...+2^{100}\right)\)

\(2C=2^2+2^3+2^4+2^5+...+2^{101}\)

\(2C-C=2^{101}-2\)

\(=>C=2^{101}-2\)

Answer 4

\(2^{2x-1}-2=C\)

\(2^{2x-1}-2=2^{101}-2\)

\(2^{2x-1}=2^{101}\)

\(=>2x-1=101\)

\(2x=101+1\)

\(2x=102\)

\(x=102:2\)

\(x=51\)

Answer 5

a) (x+1) + (x+2) +....+ (x+100) = 5750

=> ( x + x + x + ... + x ) + ( 1+ 2 + 3 + ... + 100 ) = 5750

=> 100x + (101 . 100 : 2 ) = 5750

=> 100x + 5050 = 5750

 => 100x = 5750 - 5050

  => 100x = 700

=> x = 700 : 100 

=> x = 7