zad Wykonaj działania a) (x-2x^)^= b) (x^-2x)^-(x^-2)^= c) (2x-1/2)^-(2x+1/2)^= zad2 Rozwiąż równanie a) (x-4)(x-2)=0 b) 2x^+x-6=0 c) x(x^+2)=2(x+32) d) x do 4 -12x do 3+36x^=0 zad3 Oblicz iloczyn i

Zadanie 1 [latex]a)(x-2x^2)^2=x^2-4x^3+4x^4=4x^2-4x^3+x^2 \\b)(x^2-2x)^2-(x^2-2)^2=x^4-4x^3+4x^2-x^4+4x^2-4= \\=-4x^3+8x^2-4 \\c)left ( 2x-dfrac{1}{2} ight )^2-left ( 2x+dfrac{1}{2} ight )^2=4x^2-2x+dfrac{1}{4}-4x^2-2x-dfrac{1}{4}= \\=-4x[/latex] ================================== Zadanie 2 [latex]a)(x-4)(x-2)=0 \\x-4=0 quad vee quad x-2=0 \\x=4 quad vee quad x=2 \\x in left { 2,4 ight } \\b)2x^2+x-6=0 \\Delta=1+48=49 \\sqrt{Delta}=7 \\x_1=dfrac{-1-7}{4}=-2 \\x_2=dfrac{-1+7}{4}=dfrac{3}{2} \\x in left { -2,dfrac{3}{2} ight }[/latex] [latex]c)x(x^2+2)=2(x+32) \\x^3+2x=2x+64 \\x^3+64=0 \\(x+4)(x^2-4x+16)=0 \\x-4=0 quad vee quad underbrace{x^2-4x+16}_{Delta extless 0}=0 \\x=4 quad vee quad x otin O \\x=4 \\d)x^4-12x^3+36x^2=0 \\x^2(x^2-12x+36)=0 \\x^2(x-6)^2=0 \\x^2=0 quad vee quad x-6=0 \\x=0 quad vee quad x=6 \\xinleft { 0,6 ight }[/latex] ============================ Zadanie 3 [latex](x^2-3)(x+2)=0 \\(x+sqrt{3})(x-sqrt{3})(x+2)=0 \\x+sqrt{3}=0 quad vee quad x-sqrt{3}=0 quad vee quad x+2=0 \\x=-sqrt{3}quad vee quad x=sqrt{3}quad vee quad x=-2 \\xin left { -2,-sqrt{3} ,sqrt{3} ight } \\-2cdot (-sqrt{3})cdot sqrt{3}=-2cdot (-3)=6 \\-2+(-sqrt{3})+sqrt{3}=-2[/latex]