Đáp án:
`a,`
`1 + 2 + 3 + 4 + ... + x = 5050`
`-> (x + 1) × x ÷ 2 = 5050`
`-> (x + 1) ÷ x = 5050 × 2`
`-> (x + 1) ÷ x = 10100`
`-> (x + 1) ÷ x = 100 × 101`
`-> (x + 1) ÷ x = (100 +1) × 100`
`-> x = 100`
Vậy `x = 100`
$\\$
`b,`
`2 + 4 + 6 + 8 + ... + 2x = 110`
`-> 2 ×1 + 2× 2+ 2×3+2×4+...+2×1=110`
`-> 2 [1 + 2 + 3 + 4 + ... + x] = 110`
`-> 1 + 2 + 3 + 4 + ... + x = 110 ÷ 2`
`-> (x + 1) × x ÷ 2 = 55`
`-> (x + 1) × x = 55 × 2`
`-> (x + 1) × x = 110`
`-> (x + 1) × x = 11 × 10`
`-> (x + 1) × x = (10 + 1) × 10`
`-> x = 10`
Vậy `x = 10`
$\\$
`c,`
`|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 `x = 0` hoặc `x = -10100`
