Question

1+2+3+......................x=55

tìm x

Answer 1

A = 1 + 2 + 3 +......+ x = 55 
<=> (1 + 9) + (2 + 8) + (3 + 7) + (4 + 6) + 5 +....+ x = 55 
<=> x = 55 - [(1 + 9) + (2 + 8) + (3 + 7) + (4 + 6) + 5 +....] 
<=> x = 55 - (45 + ...) 
<=> x = 10 - (....) 

Nếu x > 0 => x = 10 
Thì x < 0 => x = {-10; -20;....}

Answer 2

1+2+3+...+x=55

<=> \(\left[\left(x-1\right):1+1\right].\left(x+1\right):2=55.\)

<=>  \(x.\left(x+1\right)=55.2\)

<=>  \(x.\left(x+1\right)=110\)

<=> \(x^2+x=100+10\)

<=> \(x^2+x=10^2+10\)

<=> \(x=10\)