Bonjour,
A(x) = (5 - 2)² -(2x - 2)²
Ici tu as des identités remarquables de type: a² - b² = (a-b)(a+b)
A(x) = (5 - x - (2x - 2))*(5 - x+(2x - 2))
A(x) = (5 - x - 2x + 2)*(5 - x + 2x - 2)
A(x) = (7 - 3x)*(3 + x) -> Factorisation
A(x) = 21+7x -9x -3x²
A(x) = -3x² -2x + 21
a.
A(x)=0
-3x² -2x +21 = 0
Δ = b²- 4ac
Δ = (-2)² - 4 *(-3)*21
Δ = 4 + 252
Δ = 256
x1 = (- b - √Δ)/2a
x1 = (2 - √256)/ (-6)
x1 = (2 - 16) /(-6)
x1 = -14 / (-6)
x1 = 7/3
x2 = (2+16)/(-6)
x2 = 18/(-6)
x2 = -3
Les solutions pour A(x)=0 sont S = {-3; 7/3}
b.
A(x)= -2x
-3x² -2x + 21 = -2x
-3x² + 21 = 0
-3x² = -21
x² = -21/(-3)
x² = 7
x = √7 ou x = -√7
Les solutions de l'équation A(x) = -2x sont S = {√7; -√7}
A(0) = -3*0² +2*0 + 21
A(0) = 21
A(1/√3) = -3*(1/√3)² + 2*(1/√3) + 21
A(1/√3) = -3*(1/3) + (2√3)/3 + 21
A(1/√3) = -1 + (2√3)/3 + 21
A(1/√3) = 20 + (2√3)/3
