←Vrati se na zadatke3. ZadatakNeka je x=2(3+1)(34+1)(38+1)(316+1).x=\frac{2}{(\sqrt3+1)(\sqrt[4]{3}+1)(\sqrt[8]{3}+1)(\sqrt[16]{3}+1)}.x=(3+1)(43+1)(83+1)(163+1)2. Odredite (x+1)64(x+1)^{64}(x+1)64.Prikaži rješenjeRješenjePomnožimo brojnik i nazivnik s 316−1\sqrt[16]{3}-1163−1. x=2(316−1)(3+1)(34+1)(38+1)(316+1)(316−1)=2(316−1)(3+1)(34+1)(38+1)(38−1)=2(316−1)(3+1)(34+1)(34−1)=2(316−1)(3+1)(3−1)=2(316−1)3−1=316−1.\begin{aligned} x&=\frac{2(\sqrt[16]{3}-1)}{(\sqrt3+1)(\sqrt[4]{3}+1)(\sqrt[8]{3}+1)(\sqrt[16]{3}+1)(\sqrt[16]{3}-1)}\\ &=\frac{2(\sqrt[16]{3}-1)}{(\sqrt3+1)(\sqrt[4]{3}+1)(\sqrt[8]{3}+1)(\sqrt[8]{3}-1)}\\ &=\frac{2(\sqrt[16]{3}-1)}{(\sqrt3+1)(\sqrt[4]{3}+1)(\sqrt[4]{3}-1)}\\ &=\frac{2(\sqrt[16]{3}-1)}{(\sqrt3+1)(\sqrt3-1)}\\ &=\frac{2(\sqrt[16]{3}-1)}{3-1}=\sqrt[16]{3}-1. \end{aligned}x=(3+1)(43+1)(83+1)(163+1)(163−1)2(163−1)=(3+1)(43+1)(83+1)(83−1)2(163−1)=(3+1)(43+1)(43−1)2(163−1)=(3+1)(3−1)2(163−1)=3−12(163−1)=163−1. Tada je (x+1)64=(316−1+1)64=(316)64=34=81.(x+1)^{64}=\big(\sqrt[16]{3}-1+1\big)^{64} =\big(\sqrt[16]{3}\big)^{64}=3^4=81.(x+1)64=(163−1+1)64=(163)64=34=81.Pomakni formulu lijevo ili desno.
