rozwiaz rownanie a)x( do pot.4) - 9x (do pot 2) =0 b) x do 4 + 7x do2 =8x do 3 c) 3x do 3 -5x do2 - 6x + 10 =0

a) [latex]x^4-9x^2=0[/latex] [latex]x^2(x^2-9)=0[/latex] [latex]x^2(x-3)(x+3)=0[/latex] [latex]x^2=0 vee x-3=0 vee x+3=0[/latex] [latex]x=0 vee x=3 vee x=-3[/latex] b) [latex]x^4+7x^2=8x^3[/latex] [latex]x^4-8x^3+7x^2=0[/latex] [latex]x^2(x^2-8x+7)=0[/latex] [latex]Delta=(-8)^2-4 cdot 1 cdot 7=64-28=36[/latex] [latex]sqrt{Delta}=6[/latex] [latex]x=frac{8-6}{2}=1 vee x=frac{8+6}{2}=7[/latex] [latex]x^2(x-1)(x-7)=0[/latex] [latex]x=0 vee x=1 vee x=7[/latex] c) [latex]3x^3-5x^2-6x+10=0[/latex] [latex]x^2(3x-5)-2(3x-5)=0[/latex] [latex](3x-5)(x^2-2)=0[/latex] [latex](3x-5)(x-sqrt2)(x+sqrt2)=0[/latex] [latex]3x-5=0 vee x-sqrt2=0 vee x+sqrt2=0[/latex] [latex]3x=5 vee x=sqrt2 vee x=-sqrt2[/latex] [latex]x=frac53 vee x=sqrt2 vee x=-sqrt2[/latex]