bonsoir
6 entiers naturels consécutifs
n + n + 1 + n + 2 + n + 3 +n + 4 + n + 5
n ( n + 1 ) = 3 ( n + 2 + n + 3 + n + 4 + n + 5 )
n² + n = 3 ( 4 n + 14)
n² + n = 12 n + 42
n² + n - 12 n = 42
n² - 11 n = 42
n² - 11 n - 42 = 0
Δ = ( - 11 )² - 4 ( 1 * - 42 ) = 121 + 168 = 289 = 17²
x 1 = ( 11 - 17 ) / 2 = - 6 /2 = - 3
x 2 = ( 11 + 17 ) /2 = 28/2 = 14
14 * 15 = 3 ( 16 + 17 + 18 + 19)
210 = 3 * 70 = 210
14 ; 15 ; 16;17 ;18 ;19
