Question

Tìm x , biết:

x + 15 chia hết cho x+ 3

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

Tick nào!!!

Answer 1

x+15 chia hết cho x+3

=> x+3+12 chia hết cho x+3

=> 12 chia hết cho x+3

=> x+3 \(\in\)Ư(12)={-12; -6; -4; -3; -2; -1; 1; 2; 3; 4; 6; 12}

=> x \(\in\){-15; -9; -7; -6; -5; -4; -2; -1; 0; 1; 3; 9}

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

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

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

=> 100x+\(\frac{100+\left(100+1\right)}{2}\)=5750

=> 100x+5050=5750

=> 100x=5750-5050

=> 100x=700

=> x=700:100

Vậy x=7.

Answer 2

x e { 0;1;3 }

x = 7