Oblicz równanie : 9[latex]9x^{3}+18x^{2}-16x-32=0 27x^{3}+27x^{2}-25x-25=0[/latex]

9x³+18x²-16x-32=0 9x²(x+2)-16(x+2)=0 (x+2)(9x²-16)=0 (x+2)(3x-4)(3x+4)=0 x=-2  v   x=4/3   x=-4/3 27x³+27x²-25x-25=0 27x²(x+1)-25(x+1)=0 (x+1)(27x²-25)=0 (x+1)(3√3x-5)(3√3x+5)=0 x=-1 v x=5/9 √3  v x=-5/9 √3

9x³+18x²-16x-32 = 0 9x²(x+2)-16(x+2) = 0 (x+2)(9x²-16) = 0 (x+2)(3x+4)(3x-4) = 0 x+2 = 0   => x = -2 lub 3x+4 = 0   3x = -4  /:3 x = -4/3 x = -1⅓ lub 3x-4 = 0 3x = 4 x = 1⅓ Odp. x = -2   v   x = -1⅓   v   x = 1⅓   27x³+27x²-25x-25 = 0 27x²(x+1)-25(x+1) = 0 (x+1)(27x²-25) = 0 (x+1)(√27x+5)(√27x-5) = 0 (x+1)(3√3x+5)(3√3x-5) = 0 x+1 = 0   => x = -1 lub 3√3x+5 = 0 3√3x = -5  /:3√3 x = -5/3√3 ·√3/√3 = -5√3/9 lub 3√3x-5 = 0 3√3x = 5  /:3√3 x = 5/3√3 x = 5√3/9 Odp. x = -1   v   x = -5√3/9   v   x = 5√3/9