Bonsoir
1)
4x² = 100
4x²-100 = 0 (forme de a²-b² =(a-b)(a+b)
(2x-10)(2x+10) = 0
si l'un des facteurs est nul
2x-10 = 0 si x = 10/2 = 5
2x+10 = 0 si x = -10/2 = -5
2)
x
3x
3x+2
(3x+2)²
(3x+2)² -3²
question 1)
(3x+2)²- 3² (forme idem qu'au dessus)
(3x+2-3)(3x+2+3) = 0
(3x-1)(3x+5) = 0
3x-1 = 0 si x = 1/3
3x+5 = 0 si x = -5/3
2)
(3x-1)(3x+5) =16
9x² +15x -3x -5 = 16
9x² +12x -21 = 0
on calcule le discriminant ou delta
delta = b²-4ac = 144+756 = 900
Vdelta =V900 = 30 ( V veut dire racine )
deux solutions
x' = (-b-Vdelta)/2a = (-12 - 30)/ (2*9) = -42/18 = -7/3
x" = (-b+Vdelta) / 2a = (-12+30) /18 = 18 /18 = 1
