\(1+2+3+...+x=500500\)
\(\Rightarrow\left(x+1\right)\left[\left(x-1\right):1+1\right]:2=500500\)
\(\Rightarrow\left(x+1\right)\left(x-1+1\right):2=500500\)
\(\Rightarrow x\left(x+1\right):2=500500\)
\(\Rightarrow x\left(x+1\right)=1001000\)
\(\Rightarrow x\left(x+1\right)=1000\cdot1001\)
\(\Rightarrow x=1000\)
\(1+2+3+...+x=500500\) (ĐK: \(x>0\))
\(\dfrac{x\left(x+1\right)}{2}=500500\)
\(x\left(x+1\right)=500500.2\)
\(x^2+x=1001000\)
\(x^2+x-1001000=0\)
\(x^2-1000x+1001x-1001000=0\)
\(\left(x^2-1000x\right)+\left(1001x-1001000\right)=0\)
\(x\left(x-1000\right)+1001\left(x-1000\right)=0\)
\(\left(x-1000\right)\left(x+1001\right)=0\)
\(x-1000=0\) hoặc \(x+1001=0\)
*) \(x-1000=0\)
\(x=1000\) (nhận)
*) \(x+1001=0\)
\(x=-1001\) (loại)
Vậy \(x=1000\)