1) A = -2
B = -2*3 = -6 (* signifie multiplié par)
C = -6-1 = -7
D = -7*-7 = 49
E = 9 * (-2)² = 9*4 = 36
F = 49 - 36 = 13
2) On pose A = x
B = x*3 = 3x
C = 3x-1
D = (3x-1)² = 9x²-2*3x*1+1 = 9x²-6x+1
E = 9*x² = 9x²
F = 9x²-6x+1 - 9x² = -6x+1
Cet algorithme décrit la fonction f(x) = -6x+1
3) Si on écrit F en fonction de A on obtient :
F = -6*A + 1
donc
-6 * A + 1 = -12071
-6 * A = -12071 - 1
-6 * A = -12072
A = -12072/-6
A = 2012
