Proszę o zrowiązanie tych zadań: 1. Rozwiąż równainie [latex]frac{(x - sqrt{5})(1 + 2sqrt{5})}{2}- xsqrt{5}=0[/latex]   2. Rozwiąż równanie [latex](2x - 1)^{2} - (2x +1)^{2} = x^{2}[/latex]

zadanie 1   [latex]frac{(x-sqrt5)(1+2sqrt5)}{2} -xsqrt5 = 0/cdot 2\ (x-sqrt5)(1+2sqrt5) - 2sqrt5 x = 0\ x - sqrt5 + 2sqrt5 x - 10 - 2sqrt5 x = 0\ x -10-sqrt5=0\ x=10+sqrt5[/latex]     zadanie 2   [latex](2x-1)^2 - (2x+1)^2 = x^2\ 4x^2 - 4x +1 - (4x^2 + 4x +1) = x^2\ 4x^2 - 4x +1 - 4x^2 -4x -1 = x^2\ -8x = x^2\ x^2 + 8x = \ x(x+8)=0\ x=0\ x+8=0\ x=-8[/latex]  

zad 1. [latex]frac{(x-sqrt{5})(1+sqrt{5})}{2}-xsqrt{5}=0[/latex]   [latex](x-sqrt{5})(1+2sqrt{5})-x*2sqrt{5}=0[/latex]   [latex]x+x*2sqrt{5}-sqrt{5}-10-x*2sqrt{5}=0[/latex]   [latex]x=10+sqrt{5}[/latex]   zad 2. [latex](2x-1)^{2}-(2x+1)^{2}=x^{2}[/latex]   [latex](2x-1+2x+1)((2x-1)-(2x+1))=x^{2}[/latex]   [latex]4x*(-2)=x^{2}[/latex]   [latex]x^{2}+8x=0[/latex]   [latex]x(x+8)=0[/latex]   [latex]x=0vee x+8=0[/latex]   [latex]x=0vee x=-8[/latex]