demonstration

[invitef96bb482]

On me demande de calculer:U=80976456*80976458-80976457*80976459.la calculatrice donne 0.Comment le demontré?
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[Cherchell]

Tu poses x = 80 976 458
80976456 = x - 2
80976457 = x - 1
80976459 = x + 1
donc U = x (x - 2) - (x - 1) (x + 1)
U =x ² - 2 x - (x ² - 1)
U = 1 - 2 x
U = - 161 952 915