Rozwiąż równanie [latex]9x^{3}+18x^{2}-16x-32=0[/latex]

[latex]9x^3 + 18x^2-16x - 32 = 0\ 9x^2(x + 2) - 16(x + 2) = 0\ (9x^2 - 16)(x + 2) = 0\ 9x^2 = 16 vee x = -2\ x^2 = frac{16}{9}\ x = -frac{4}{3} vee x = frac{4}{3} vee x = -2\[/latex]

[latex]9x^3+18x^2-16x-32=0[/latex] [latex]9x^2 cdot (x +2)-16 cdot (x+2)=0[/latex] [latex](x +2)(9x^2 -16)=0[/latex] [latex](x +2)[(3x)^2 -4^2]=0[/latex] [latex](x +2)(3x -4)(3x+4)=0[/latex] [latex]x +2 = 0 vee 3x - 4 = 0 vee 3x+4 = 0[/latex]   [latex]x +2 = 0[/latex] [latex]x = - 2[/latex] [latex]3x - 4 = 0[/latex] [latex]3x = 4 /:3[/latex] [latex]x = frac{4}{3}[/latex] [latex]x = 1frac{1}{3}[/latex]   [latex]3x + 4 = 0[/latex] [latex]3x = - 4 /:3[/latex] [latex]x = -frac{4}{3}[/latex] [latex]x = - 1frac{1}{3}[/latex]   Odp. x = - 2 lub x = -1⅓ lub x = 1⅓.