Bonjour,
Exercice n°3 :
[tex]1) \: \: \: (x - 9) {}^{2} - (7x + 6)(x - 9)[/tex]
[tex] = {x}^{2} - 18x + 81 - 7 {x}^{2} - 63x + 6x - 54[/tex]
[tex] = - 6 {x}^{2} + 39x + 135[/tex]
[tex]2) \: \: \: (x - 9) {}^{2} - (7x + 6)(x - 9)[/tex]
[tex] = (x - 9)( - (7x + 6) + x - 9)[/tex]
[tex] = (x - 9)( - 7x - 6 + x - 9)[/tex]
[tex] = (x - 9)( - 6x - 15)[/tex]
[tex] = 3(x - 9)( - 2x - 5)[/tex]
3) -6 × (-5/4)^2 + 39 × (-5/4) + 135
= -150/16 - 195/4 + 135
= (-2 × 75)/(2 × 8) - 195/4 + 135
= - 75/8 - 390/8 + 135
= -475/8 + 135
= -475/8 + (8 × 135)/8
= -475/8 + 1080/8
= 615/8
[tex]4) \: \: \: - 3( x - 9)(2x + 5) = 0[/tex]
[tex](x - 9)(2x + 5) = 0[/tex]
[tex]x - 9 = 0 \: \: \: ou \: \: \: 2x + 5 = 0[/tex]
[tex]x = 9 \: \: \: ou \: \: \: x = - \frac{5}{2} [/tex]
