Réponse :
Explications étape par étape
Bonjour
Avec a et b > 0
A - B = ab - 1 - (a + 1)(b + 1)
A - B = ab - 1 - ab - a - b - 1
A - B = -a - b - 2 < 0
A - B < 0
A < B
A - B = a/b + b/a - 2
A - B = (a^2 + b^2 - 2ab)/ab
A - B = (a - b)^2/ab
A - B > 0
A > B
A - B = 1/a + 1/b - 4/(a + b)
A - B = [b(a + b) + a(a + b) - 4ab]/[ab(a + b)]
A - B = (ab + b^2 + a^2 + ab - 4ab)/[ab(a + b)]
A - B = (a^2 - 2ab + b^2)/[ab(a + b)]
A - B = (a - b)^2/[ab(a + b)]
A - B > 0
A > 0
A - B = (7a + 2b)/7a - 8b/(7a + 2b)
A - B = [(7a + 2b)^2 - 8b * 7a)/[7a(7a + 2b)]
A - B = (49a^2 + 28ab + 4b^2 - 56ab)/[7a(7a + 2b)]
A - B = [(7a)^2 - 2 * 7a * 2b + (2b)^2]/[7a(7a + 2b)]
A - B = (7a - 2b)^2/[7a(7a + 2b)]
A - B > 0
A > B
