[latex]frac{1}{frac{(sqrt{6}+sqrt{2}-2)^2}{4}} + frac{1}{ frac{(sqrt{6}-sqrt{2}+2)^2}{4} } = frac{4}{(sqrt{6}+sqrt{2}-2)^2} + frac{4}{(sqrt{6}-(sqrt{2}-2))^2} Niech: \ a=sqrt{6} \ b=sqrt{2}-2 \ Wtedy:\ \ frac{4}{(a+b)^2} + frac{4}{(a-b)^2} = frac{4(a-b)^2}{(a+b)^2(a-b)^2} + frac{4(a+b)^2}{(a+b)^2(a-b)^2}\frac{4(a-b)^2}{(a+b)^2(a-b)^2} + frac{4(a+b)^2}{(a+b)^2(a-b)^2} = frac{4(a^2-2ab+b^2)+4(a^2+2ab+b^2)}{(a+b)^2(a-b)^2} = \ \ = frac{8a^2+8b^2}{((a+b)(a-b))^2}=frac{8a^2+8b^2}{(a^2-b^2)^2}\8a^2 = 8(sqrt{6})^2 = 8 * 6 =48 \ 8b^2 = 8(sqrt{2}-2)^2 = 8(2-4sqrt{2}+4) = 16-32sqrt{2}+32=48-32sqrt{2}\ licznik:\ 8a^2-8b^2=48-48+32sqrt{2}=32sqrt{2} \ mianownik:\ (a^2-b^2)^2 = ((sqrt{6})^2-(sqrt{2}-2)^2)^2=(6-(2-4sqrt{2}+4))^2=\ =(6-(6-4sqrt{2}))^2=(4sqrt{2})^2=32\ frac{32sqrt{2}}{32} = sqrt{2}[/latex]
