[laTEX]x^3 -ax^2-3ax+4 \\ \\ y' = 0 \Leftrightarrow 3x^2-2ax-3a =0 \\ \\ \Delta ' = a^2 +9a > 0 \Rightarrow a < -9 , a > 0 \\ \\ 3x_1^2-2ax_1-3a =0 \\ \\ 3x_2^2-2ax_2-3a =0 \\ \\ x_1+x_2 = \frac{2a}{3} \\ \\ x_1.x_2 = -a \\ \\ mat-khac : x_1^2 +2ax_2 +9a = (3x_1^2 -2ax_1 -3a) -2x_1^2 + 2ax_1+2ax_2 + 12a \\ \\ -2x_1^2 +2a(x_1+x_2) +12a = -2x_1^2 + \frac{4a^2}{3} +12a\\ \\ x_2^2 +2ax_1 +9a = (3x_2^2 -2ax_2 -3a) -2x_2^2 + 2ax_1+2ax_2 + 12a \\ \\ -2x_2^2 +2a(x_1+x_2) +12a = -2x_2^2 + \frac{4a^2}{3} +12a \\ \\[/latex]
[laTEX] mat-khac : 3x_1^2 = 2ax_1+3a \Rightarrow -2x_1^2 = - \frac{2}{3}(2ax_1+3a) \\ \\ \Rightarrow -2x_1^2 + \frac{4a^2}{3} +12a = - \frac{2}{3}(2ax_1+3a) + \frac{4a^2}{3} +12a \\ \\ - \frac{2}{3}(2ax_2+3a) + \frac{4a^2}{3} +12a \\ \\ \Rightarrow \frac{x_1^2 +2ax_2 +9a }{a^2} = \frac{- \frac{2}{3}(2ax_1+3a) + \frac{4a^2}{3} +12a }{a^2} = \frac{- \frac{2}{3}(2x_1+3) + \frac{4a}{3} +12 }{a} \\ \\ \frac{a^2 }{x_2^2 +2ax_1 +9a} = \frac{ a^2}{- \frac{2}{3}(2ax_2+3a) + \frac{4a^2}{3} +12a} = \frac{ a}{- \frac{2}{3}(2x_2+3) + \frac{4a}{3} +12}[/laTEX]