a) 2x⁴-2-5x³+5x=0 2(x⁴-1)-5x(x²-1)=0 2(x²-1)(x²+1) -5x(x²-1)=0 (x²-1)(2(x²+1) -5x)=0 (x-1)(x+1)(2x²-5x+2)=0 (x-1)=0 ∨ (x+1)=0∨ 2x²-5x+2=0 x=1 ∨ x= -1 ∨ Δ=25-16=9 √9=3 x₁=½ x₂=2 b) 12x⁴ -12+7x³+7x=0 12(x⁴-1)+7x(x²-1)=0 12(x²-1)(x²+1) +7x(x²-1)=0 (x²-1)(12(x²+1) +7x)=0 (x-1)(x+1)(12x²+7x+12)=0 (x-1)=0 ∨ (x+1)=0∨ 12x²+7x+12=0 x=1 ∨ x= -1 ∨ Δ=49-576= -527 brak rozwiazań { -1,1} C) x³-2x²-16x+32=0 x²(x-2)-16(x-2)=0 (x-2)(x²-16)=0 (x-2)(x-4)(x+4)=0 x=2 x=4 x= -4 {-4,2,,4}
a) 2x⁴ - 5x³ + 5x -2 = 0 x^{3}( 2x-5)+(5x-2) x^{3}=0 x=0 2x-5+5x-2=0 7x=7 x=1 odp x_{1}= 0; x_{2}=1 b)12x⁴ + 7x³ + 7x - 12 = 0 12x⁴-12+7x³ + 7x=0 12(x⁴-1)cdot7x(x^{2}+1) (12+7x)(x⁴-1)(x^{2}+1) 12+7x=0 7x=-12 x=frac{7}{12} x⁴-1=0 x=1 x^{2}+1=0 x=-1 odp x_{1}= frac{7}{12}; x_{2}=1; x_{3}=-1 c)x³ - 2x² - 16x - 32 = 0 (x²-16)(x-2)(x+2) x=4, x=2, x=-2
