Bonjour
on considère l'expression f(x)=(3x+1)^2 -2(x+2)(3x+1)
1 factoriser f(x)
f(x) = (3x + 1)[3x + 1 - 2(x + 2)]
f(x) = (3x + 1)(3x + 1 - 2x - 2)
f(x) = (3x + 1)(x - 1)
2 developer f(x)
f(x) = 9x^2 + 6x + 1 - 2(3x^2 + x + 6x + 2)
f(x) = 9x^2 - 6x^2 + 6x - 14x + 1 - 4
f(x) = 3x^2 - 8x - 3
3 resoudre les équations f(x)=0 ; F(X)= -3
• (3x + 1)(x - 1) = 0
3x + 1 = 0 ou x - 1 = 0
3x = -1 ou x = 1
x = -1/3 ou x = 1
• 3x^2 - 8x - 3 = -3
3x^2 - 8x = -3 + 3
3x^2 - 8x = 0
x(3x - 8) = 0
x = 0 ou 3x - 8 = 0
x = 0 ou 3x = 8
x = 0 ou x = 8/3
4 calculer f(1) ; f (racine carree de 2 )
f(1) = (3 * 1 + 1)(1 - 1) = 4 * 0 = 0
[tex]f(\sqrt2) = 3 \times (\sqrt2)^{2} - 8 \sqrt2 - 3[/tex]
[tex]f(\sqrt2) = 6 - 8\sqrt2 - 3[/tex]
[tex]f(\sqrt2) = 3 - 8\sqrt2[/tex]
