Hướng dẫn trả lời:
`{2}/{sqrt{3} - 1} + {1}/{sqrt{3}} - sqrt{27}`
`= {2cdot(sqrt{3} + 1)}/{(sqrt{3} - 1)cdot(sqrt{3} + 1)} + {1}/{sqrt{3}} - sqrt{3^3}`
`= {2cdot(sqrt{3} + 1)}/{(sqrt{3})^2 - 1^2} + {1}/{sqrt{3}} - 3sqrt{3}`
`= {2cdot(sqrt{3} + 1)}/{3 - 1} + {1}/{sqrt{3}} - 3sqrt{3}`
`= {2cdot(sqrt{3} + 1)}/{2} + {1}/{sqrt{3}} - 3sqrt{3}`
`= (sqrt{3} + 1) + {1}/{sqrt{3}} - 3sqrt{3}`
`= {3cdot(sqrt{3} + 1)}/{3} + {sqrt{3}}/{(sqrt{3})^2} - {3cdot sqrt{3}}/(sqrt3)^2`
`= {3sqrt{3} + 3}/{3} + {sqrt{3}}/{3} - {9sqrt{3}}/3`
`= {3sqrt{3} + 3 + sqrt{3} - 9sqrt{3}}/3`
`= {3 + (3sqrt{3} + sqrt{3} - 9sqrt{3})}/3`
`= {3 - 5sqrt{3}}/3`
Đáp án:
`= {3 - 5sqrt{3}}/3`
