on considere l'expression a=(12x+7)²-(11-5x)(12x+7) developer a factoriser a calculer a pour x= - [tex]\frac{5}{12}[/tex] Merci et bonne fete

Bonjour,

1) Développer A :

A = (12x+7)²-(11-5x)(12x+7)

↳ Identité remarquable : (a+b)² = a²+2ab+b²

A = 144x²+168x+49-(11-5x)(12x+7)

A = 144x²+168x+49-(132x+77-60x²-35x)

A = 144x²+168x+49-(97x+77-60x²)

A = 144x²+168x+49-97x-77+60x²

A = 204x²+168x+49-97x-77

A = 204x²+71x+49-77

A = 204x²+71x-28

2) Factoriser A :

A = (12x+7)²-(11-5x)(12x+7)

A = (12x+7)(12x+7-(11-5x))

A = (12x+7)(12x+7-11+5x))

A = (12x+7)(17x+7-11)

A = (12x+7)(17x-4)

3) Calculer A pour x = -5/12

A = (12x+7)²-(11-5x)(12x+7)

A = (12×-5/12+7)²-(11-5×-5/12)(12×-5/12+7)

A = (-5+7)²-(11+25/12)(-5+7)

A = 2²-(11+25/12)(-5+7)

A = 2²-157/12×(-5+7)

A = 2²-157/12×2

A = 2²-157/6

A = 4-157/6

A = -133/6

/ = fraction.

Bonne journée.