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![\sqrt[3]{2- \sqrt{5} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2-+%5Csqrt%7B5%7D+%7D+ "\sqrt[3]{2- \sqrt{5} }")
+ ![\sqrt[3]{2+ \sqrt{5} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2%2B+%5Csqrt%7B5%7D+%7D+ "\sqrt[3]{2+ \sqrt{5} }")
![\\ $Anggap:$ \\ a=\sqrt[3]{2-\sqrt{5}} \\ b=\sqrt[3]{2+\sqrt{5}} \\ a^3+b^3=(a+b)(a^2-ab+b^2) \\ \displaystyle a+b=\frac{a^3-b^3}{a^2-ab+b^2} \\ a+b=\frac{2-\sqrt{5}+2+\sqrt{5}}{\sqrt[3]{(2-\sqrt{5})^2}-\sqrt[3]{(2-\sqrt{5})(2+\sqrt{5})}+\sqrt[3]{(2+\sqrt{5})^2}} \\ \\ a+b=\frac{4}{\sqrt[3]{9-4\sqrt{5}}-\sqrt[3]{-1}+\sqrt[3]{9+4\sqrt{5}}} \\ \\ a+b=\frac{4}{1+\frac{1}{2}(3-\sqrt{5})+\frac{1}{2}(3+\sqrt{5})} \\ \\ a+b=\frac{4}{1+\frac{3}{2}+\frac{3}{2}} \\ \\ a+b=\frac{4}{4} \\ a+b=1](https://tex.z-dn.net/?f=%5C%5C+%24Anggap%3A%24+%5C%5C+a%3D%5Csqrt%5B3%5D%7B2-%5Csqrt%7B5%7D%7D+%5C%5C+b%3D%5Csqrt%5B3%5D%7B2%2B%5Csqrt%7B5%7D%7D+%5C%5C+a%5E3%2Bb%5E3%3D%28a%2Bb%29%28a%5E2-ab%2Bb%5E2%29+%5C%5C+%5Cdisplaystyle+a%2Bb%3D%5Cfrac%7Ba%5E3-b%5E3%7D%7Ba%5E2-ab%2Bb%5E2%7D+%5C%5C+a%2Bb%3D%5Cfrac%7B2-%5Csqrt%7B5%7D%2B2%2B%5Csqrt%7B5%7D%7D%7B%5Csqrt%5B3%5D%7B%282-%5Csqrt%7B5%7D%29%5E2%7D-%5Csqrt%5B3%5D%7B%282-%5Csqrt%7B5%7D%29%282%2B%5Csqrt%7B5%7D%29%7D%2B%5Csqrt%5B3%5D%7B%282%2B%5Csqrt%7B5%7D%29%5E2%7D%7D+%5C%5C+%5C%5C+a%2Bb%3D%5Cfrac%7B4%7D%7B%5Csqrt%5B3%5D%7B9-4%5Csqrt%7B5%7D%7D-%5Csqrt%5B3%5D%7B-1%7D%2B%5Csqrt%5B3%5D%7B9%2B4%5Csqrt%7B5%7D%7D%7D+%5C%5C+%5C%5C+a%2Bb%3D%5Cfrac%7B4%7D%7B1%2B%5Cfrac%7B1%7D%7B2%7D%283-%5Csqrt%7B5%7D%29%2B%5Cfrac%7B1%7D%7B2%7D%283%2B%5Csqrt%7B5%7D%29%7D+%5C%5C+%5C%5C+a%2Bb%3D%5Cfrac%7B4%7D%7B1%2B%5Cfrac%7B3%7D%7B2%7D%2B%5Cfrac%7B3%7D%7B2%7D%7D+%5C%5C+%5C%5C+a%2Bb%3D%5Cfrac%7B4%7D%7B4%7D+%5C%5C+a%2Bb%3D1 "\\ $Anggap:$ \\ a=\sqrt[3]{2-\sqrt{5}} \\ b=\sqrt[3]{2+\sqrt{5}} \\ a^3+b^3=(a+b)(a^2-ab+b^2) \\ \displaystyle a+b=\frac{a^3-b^3}{a^2-ab+b^2} \\ a+b=\frac{2-\sqrt{5}+2+\sqrt{5}}{\sqrt[3]{(2-\sqrt{5})^2}-\sqrt[3]{(2-\sqrt{5})(2+\sqrt{5})}+\sqrt[3]{(2+\sqrt{5})^2}} \\ \\ a+b=\frac{4}{\sqrt[3]{9-4\sqrt{5}}-\sqrt[3]{-1}+\sqrt[3]{9+4\sqrt{5}}} \\ \\ a+b=\frac{4}{1+\frac{1}{2}(3-\sqrt{5})+\frac{1}{2}(3+\sqrt{5})} \\ \\ a+b=\frac{4}{1+\frac{3}{2}+\frac{3}{2}} \\ \\ a+b=\frac{4}{4} \\ a+b=1")
