bonjour
f(x) = (4x - 5)² - (3x - 1)(4x - 5)
a) Factoriser f(x)
f(x) = (4x - 5)² - (3x - 1)(4x - 5) [ a² = a*a ]
f(x) = (4x - 5)(4x - 5) - (3x - 1)(4x - 5) facteur commun (4x - 5)
f(x) = (4x - 5)(4x - 5) - (3x - 1)(4x - 5)
f(x) = (4x - 5)[(4x - 5) - (3x - 1)]
f(x) = (4x - 5)(4x - 5 - 3x + 1)
f(x) = (4x - 5)(x - 4)
b) Résoudre l'équation f(x) = 0
f(x) = 0 <=> (4x - 5)(x - 4) = 0 équation produit nul
<=> 4x - 5 = 0 ou x - 4 = 0
4x = 5 x = 4
x = 5/4
S = {5/4 ; 4}
