Toán (4+ $\sqrt[]{15}$ ).( $\sqrt[]{10}$ – $\sqrt[]{6}$ ). $\sqrt[]{4-\sqrt[]{15}}$ = 2 08/07/2021 By Quinn (4+ $\sqrt[]{15}$ ).( $\sqrt[]{10}$ – $\sqrt[]{6}$ ). $\sqrt[]{4-\sqrt[]{15}}$ = 2
`(4+\sqrt{15})(\sqrt{10}-\sqrt{6}).\sqrt{4-\sqrt{15}}` `=\sqrt{(4+\sqrt{15})^2}.(\sqrt{10}-\sqrt{6}).\sqrt{4-\sqrt{15}}` `=(\sqrt{4+\sqrt{15}}. \sqrt{4-\sqrt{15}}). \sqrt{4+\sqrt{15}}. \sqrt{2}.(\sqrt{5}-\sqrt{3})` `=\sqrt{16-15}. \sqrt{8+2\sqrt{15}}.(\sqrt{5}-\sqrt{3})` `=\sqrt{(\sqrt{5}+\sqrt{3})^2}.(\sqrt{5}-\sqrt{3})` `=(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})` `=5-3` `=2` Trả lời
Đáp án: `(4+\sqrt{15})(\sqrt{10}-sqrt6).\sqrt{4-\sqrt{15}` `=\sqrt{4+\sqrt{15}}^2.\sqrt{4-\sqrt{15}}(\sqrt{10}-sqrt6)` `=\sqrt{(4+\sqrt{15})(4-\sqrt{15})}.(\sqrt{10}-sqrt6).\sqrt{4+\sqrt{15}}` `=\sqrt{16-15}.\sqrt2(\sqrt5-sqrt3).\sqrt{4+\sqrt{15}` `=1.(\sqrt5-sqrt3).\sqrt{8+2\sqrt{15}` `=(sqrt5-sqrt3)sqrt{5+2sqrt{3.5}+3}` `=(sqrt5-sqrt3)sqrt{(sqrt5+sqrt3)^2}` `=(sqrt5-sqrt3)(sqrt5+sqrt3)` `=5-3=2(Đpcm)`. Trả lời
`(4+\sqrt{15})(\sqrt{10}-\sqrt{6}).\sqrt{4-\sqrt{15}}`
`=\sqrt{(4+\sqrt{15})^2}.(\sqrt{10}-\sqrt{6}).\sqrt{4-\sqrt{15}}`
`=(\sqrt{4+\sqrt{15}}. \sqrt{4-\sqrt{15}}). \sqrt{4+\sqrt{15}}. \sqrt{2}.(\sqrt{5}-\sqrt{3})`
`=\sqrt{16-15}. \sqrt{8+2\sqrt{15}}.(\sqrt{5}-\sqrt{3})`
`=\sqrt{(\sqrt{5}+\sqrt{3})^2}.(\sqrt{5}-\sqrt{3})`
`=(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})`
`=5-3`
`=2`
Đáp án:
`(4+\sqrt{15})(\sqrt{10}-sqrt6).\sqrt{4-\sqrt{15}`
`=\sqrt{4+\sqrt{15}}^2.\sqrt{4-\sqrt{15}}(\sqrt{10}-sqrt6)`
`=\sqrt{(4+\sqrt{15})(4-\sqrt{15})}.(\sqrt{10}-sqrt6).\sqrt{4+\sqrt{15}}`
`=\sqrt{16-15}.\sqrt2(\sqrt5-sqrt3).\sqrt{4+\sqrt{15}`
`=1.(\sqrt5-sqrt3).\sqrt{8+2\sqrt{15}`
`=(sqrt5-sqrt3)sqrt{5+2sqrt{3.5}+3}`
`=(sqrt5-sqrt3)sqrt{(sqrt5+sqrt3)^2}`
`=(sqrt5-sqrt3)(sqrt5+sqrt3)`
`=5-3=2(Đpcm)`.