Đáp án:
`x=100`
`x=10`
\(\left[ \begin{array}{l}x=0\\x=(-10100)\end{array} \right.\)
Giải thích các bước giải:
`1+2+3+4+...+x=5050`
`{(x-1).[(x+1):1+1]}/2=5050`
`{(x+1).[x-1+1]}/2=5050`
`{x.(x+1)}/2=5050`
`x.(x+1)=5050.2`
`x.(x+1)=10100`
`x.(x+1)=100.101`
`=>`\(\left[ \begin{array}{l}x=100\\x+1=101\end{array} \right.\) `=>x=100`
Vậy `x=100`
$2+4+6+8+...+2x=110\\\text{Ta có:}\\2=2.1\\4=2.2\\6=2.3\\8=2.4\\.......\\2x=2.x\\`=>`2.1+2.2+2.3+2.4+...+2.x=110\\2(1+2+3+4+...+x)=110\\1+2+3+4+...+x=110:2\\1+2+3+4+...+x=55\\\frac{(x+1).[(x+1):1+1]}{2}=55\\\frac{(x+1).[x-1+1]}{2}=55\\\frac{x.(x+1)}{2}=55\\x.(x+1)=55.2\\x.(x+1)=110\\x.(x+1)=10.11\\⇒\left[ \begin{array}{l}x=10\\x+1=11\end{array} \right.⇒x=10\\\text{Vậy x=10}$
`|x+5050|=5050`
`=>`\(\left[ \begin{array}{l}x+5050=5050\\x+5050=(-5050)\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=5050-5050\\x=(-5050)-5050\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=0\\x=(-10100)\end{array} \right.\)
Vậy \(\left[ \begin{array}{l}x=0\\x=(-10100)\end{array} \right.\)
