I]
1) x² - 7x = [tex] (x- \frac{7}{2})^{2} - \frac{49}{4}[/tex]
2) x² + 2x - 3 = [tex] (x+1)^2 - 4[/tex]
3) 3x² - 5x + 5 = [tex]3(x+\frac{5}{6})^{2} - \frac{25}{12}[/tex]
II]
4) (x + 1)² = 10 x² + 10x
[tex](x + 1)^2 = 10x(x + 1)[/tex]
[tex](x + 1)^2 - 10x(x + 1) =0[/tex]
[tex](x + 1)(x+1- 10x) =0 [/tex]
[tex](x + 1)(1-9x) =0[/tex]
2 solutions possibles :
[tex]x = -1[/tex]
ou
[tex]x = \frac{1}{9}[/tex]
5) ( x - 5)² - 4 = x - 7
[tex](x - 5 + 2)(x - 5 - 2) = x - 7 [/tex]
[tex](x - 3)(x - 7) - (x - 7) = 0 [/tex]
[tex](x - 3 - 1)(x - 7) = 0 [/tex]
[tex](x - 4)(x - 7) = 0 [/tex]
2 solutions :
[tex] x = 4[/tex] ou [tex] x = 7 [/tex]
en espérant t'avoir aidé.
