3. [latex]T^2=(2x+3)^2=4x^2+12x+9[/latex] [latex]S-T^2=2x^3+x^2-3-(4x^2+12x+9)=2x^3+x^2-2-4x^2-12x-9=\ 2x^3-3x^2-12x-12[/latex] Dla x=-2 otrzymujemy [latex]2cdot(-2)^3-3cdot(-2)^2-12cdot(-2)-12=-16-12+24-12=-16[/latex] 4. a) [latex](x^2-4)(2x-3)=0 iff x^2-4=0vee{2x}-3=0 iff x=pm2vee{x}=frac{3}{2}[/latex] b) [latex]x^3-6x^2+8x=0 iff x(x^2-6x+8)=0 iff x=0vee{x^2}-6x+8=0 iff[/latex] [latex]x=0vee{x}=2vee{x}=4[/latex]
3. S = 2x³ + x² - 3 T = 2x + 3 S - T² = 2x³ + x² - 3 - (2x + 3)² = 2x³ + x² - 3 - (4x² + 12x + 9) = = 2x³ + x² - 3 - 4x² - 12x - 9 = 2x³ - 3x² - 12x - 12 dla x = -2 S - T² = 2·(-2)³ - 3·(-2)² - 12·(-2) -12 = 2·(-8) - 3·4 + 24 - 12 = -16 4. a) (x² - 4)(2x - 3) = 0 (x + 2)(x - 2)(2x - 3) = 0 x+2 = 0 v x-2 = 0 v 2x-3 = 0 x = -2 v x = 2 v x = 1,5 x ∈ {-2;1,5; -2} b) x³ - 6x² + 8x = 0 x(x² - 6x + 8) = 0 x(x² - 4x - 2x + 8) = 0 x[x(x - 4) - 2(x - 4)] = 0 x(x - 2)(x - 4) = 0 x = 0 v x-2 = 0 v x-4 = 0 x = 0 v x = 2 v x = 4 x ∈ {0,2,4}
