Tính. `(3+sqrt(5))(sqrt(10)-sqrt(2))sqrt(3-sqrt(5)` Em cảm ơn trước ạ! 03/07/2021 Bởi Josephine Tính. `(3+sqrt(5))(sqrt(10)-sqrt(2))sqrt(3-sqrt(5)` Em cảm ơn trước ạ!
`(3+\sqrt{5})(\sqrt{10}-\sqrt{2})\sqrt{3-\sqrt{5}}` `=(3+\sqrt{5})(\sqrt{10}-\sqrt{2})\sqrt{\frac{6-2\sqrt{5}}{2}}` `=(3+\sqrt{5})(\sqrt{10}-\sqrt{2})\sqrt{\frac{(\sqrt{5}-1)^2}{2}}` `=(3+\sqrt{5})(\sqrt{5}-1)\sqrt{2}.\frac{|\sqrt{5}-1|}{\sqrt{2}}` `=(3+\sqrt{5})(\sqrt{5}-1)(\sqrt{5}-1)` `=\frac{6+2\sqrt{5}}{2}(\sqrt{5}-1)^2` `=\frac{1}{2}(\sqrt{5}+1)^2.(\sqrt{5}-1)^2` `=\frac{1}{2}(5-1)^2` `=8` Bình luận
`(3+\sqrt{5})(\sqrt{10}-\sqrt{2})\sqrt{3-\sqrt{5}}`
`=(3+\sqrt{5})(\sqrt{10}-\sqrt{2})\sqrt{\frac{6-2\sqrt{5}}{2}}`
`=(3+\sqrt{5})(\sqrt{10}-\sqrt{2})\sqrt{\frac{(\sqrt{5}-1)^2}{2}}`
`=(3+\sqrt{5})(\sqrt{5}-1)\sqrt{2}.\frac{|\sqrt{5}-1|}{\sqrt{2}}`
`=(3+\sqrt{5})(\sqrt{5}-1)(\sqrt{5}-1)`
`=\frac{6+2\sqrt{5}}{2}(\sqrt{5}-1)^2`
`=\frac{1}{2}(\sqrt{5}+1)^2.(\sqrt{5}-1)^2`
`=\frac{1}{2}(5-1)^2`
`=8`
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