Tìm x: 1+2+3+4+…+x=5050 2+4+6+8+…+2x=110 |x+5050|=5050

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`