a) x³+9x-10=0 x³-x+10x-10=0 x(x²-1)+10(x-1)=0 x(x+1)(x-1)+10(x-1)=0 (x-1)*(x²+x+10)=0 Δ1-40=-39<0 II nawias nie ma m.z. x-1=0 x=1 b) x⁴-10x²+9=0 x⁴-x² - 9x² + 9=0 x²(x²-1)-9(x²-1)=0 (x²-1)(x²-9)=0 (x+1)(x-1)(x+3)(x-3)=0 x∈{-3, -1, 1, 3} c) (2x-1)(x+3)(x-2)-2(x²+6)=0 (2x-1)(x²-2x+3x-6)-2x²-12=0 2x³+2x²-12x-x²-x+6-2x²-12=0 2x³-x²-13x-6=0 W(3)=0 2x²(x-3)+5x(x-3)+2(x-3)=0 (x-3)(2x²+5x+2)=0 (x-3)(2x²+4x+x+2)=0 (x-3)*[2x(x+2)+(x+2)]=0 (x-3)(x+2)(2x+1)=0 x-3=0 v x+2=0 v 2x+1=0 x∈{-2, -1/2, 3} d) (x-4)(-3x²-x-16)-60=0 -3x³-x²-16x+12x²+4x+64-60=0 -3x³+11x²-12x+4=0 W(1)=0 -3x²(x-1)+8x(x-1)-4(x-1)=0 -(3x²-8x+4)*(x-1)=0 /:(-1) (3x²-6x-2x+4)*(x-1)=0 [3x(x-2)-2(x-2)]*(x-1)=0 (x-1)(x-2)(3x-2)=0 x-1=0 v x-2=0 v 3x-2=0 x∈{2/3, 1, 2} e) (x²-5)(x+5)-3(x-2)(x²+4)+7=0 x³+5x²-5x-25-3x³-12x+6x²+24+7=0 -2x³+11x²-17x+6=0 W(2)=0 -2x²(x-2)+7x(x-2)-3(x-2)=0 /*(-1) (x-2)(2x²-7x+3)=0 (x-2)(2x²-x-6x+3)=0 (x-2)*[x(2x-1)-3(2x-1)]=0 (x-2)(2x-1)(x-3)=0 x-2=0 v 2x-1=0 v x-3=0 x∈{1/2, 2, 3}
