Réponses

2013-12-24T12:09:06+01:00
A) (x² - 2x + 2)(x² + 2x + 2) = ((x² + 2 ) - 2x)((x² + 2) + 2x) = (x² + 2)² - 4x² = x^4 + 4x² + 4 - 4x² = x^4 + 4 
b) 1/(1 + V5) + 1/(3 +V5) =  (3 + V5 + 1 + V5)/(1+V5)(3 + V5) = (4+2V5)/(8+4V5)
=   (4+2V5)/2(4+2V5) = 1/2
1/(1-V5) + 1/(3-V5) = (3-V5+1-V5)/(1-V5)(3-V5) = (4-2V5)/(8 -4V5)
= (4-2V5)/2(4-2V5) = 1/2
les deux expressions sont égalrs car égales à 1/2
c) il faut que x > 1 
[(V(x+1)-V(x-1))²+ (V(x+1)+V(x-1))²]/(V(x+1)-V(x-1)) (V(x+1)+V(x-1)) = 3
[2(x+1)+2(x-1)]/x+1-x+1) = 3 => 4x/2 = 3 => 2x = 3 => x = 3/2
joyeux Noel!