1) A = (x – 3)2 – (x – 1)(x – 2)
A = x2-6x+9– (x2 – 2x – x + 2)
A=x2 – 6x +9 – x2 + 2x + x – 2
A= -3x + 7
2) On utilise le résultat obtenu à la question 1 en posant x = 100 000.
On remarque alors que
x – 3 = 99 997
x – 1 = 99 999
x – 2 = 99 998
Donc, comme (x – 3)2 – (x – 1)(x – 2) = –3x +7, on obtient
99 9972 – 99 999 × 99 998 = –3 × 100 000 + 7
