Bonsoir,
1) x=3
a) AB = 2(3)+1 = 7 cm
AF = 3+3 = 6 cm
b) aire FECD = CD × EC = 7 × (7-6) = 7 cm²
2) a) FD = (2x+1)-(x+3) = x-2
b) aire FECD = FD × CD = (x-2)(2x+1)
c) aire ABCD = (2x+1)²
aire ABEF = (2x+1)(x+3)
d) aire FECD = aire ABCD - aire ABEF = (2x+1)²-(2x+1)(x+3)
e) cette égalité traduit une factorisation
(2x+1)²-(2x+1)(x+3) = (2x+1)(2x+1)-(2x+1)(x+3)
= (2x+1)[(2x+1)-(x+3)]
= (2x+1)(x-2)
