Hướng dẫn trả lời:
Bài 3:
a) `{1}/{sqrt3 - sqrt2} + {1}/{sqrt3 + sqrt2}`
`= {sqrt3 + sqrt2}/{(sqrt3 + sqrt2)cdot(sqrt3 - sqrt2)} + {sqrt3 - sqrt2}/{(sqrt3 + sqrt2)cdot(sqrt3 - sqrt2)}`
`= {(sqrt3 + sqrt2) + (sqrt3 - sqrt2)}/{(sqrt3 + sqrt2)cdot(sqrt3 - sqrt2)}`
`= {sqrt3 + sqrt2 + sqrt3 - sqrt2}/{(sqrt3)^2 - (sqrt2)^2}`
`= {(sqrt3 + sqrt3) + (sqrt2 - sqrt2)}/{3 - 2}`
`= {2sqrt3}/{1}`
`= 2sqrt3`
b) `({sqrt6 - sqrt2}/{1 - sqrt3} - {5}/{sqrt5}) ÷ 1/{sqrt5 - sqrt2}`
`= ({sqrt2cdot(sqrt3 - 1)}/{1 - sqrt3} - {(sqrt5)^2}/{sqrt5}) ÷ 1/{sqrt5 - sqrt2}`
`= ({-sqrt2cdot(1 - sqrt3)}/{1 - sqrt3} - sqrt5) ÷ 1/{sqrt5 - sqrt2}`
`= (-sqrt2 - sqrt5) ÷ 1/{sqrt5 - sqrt2}`
`= - (sqrt5 + sqrt2)cdot{sqrt5 - sqrt2}/1`
`= - (sqrt5 + sqrt2)cdot(sqrt5 - sqrt2)`
`= - [(sqrt5)^2 - (sqrt2)^2]`
`= - (5 - 2)`
`= - 3`
c) `{1}/{sqrt3 + sqrt2 - sqrt5} - {1}/{sqrt3 + sqrt2 + sqrt5}`
`= {sqrt3 + sqrt2 + sqrt5}/{(sqrt3 + sqrt2 - sqrt5)cdot(sqrt3 + sqrt2 + sqrt5)} - {sqrt3 + sqrt2 - sqrt5}/{(sqrt3 + sqrt2 - sqrt5)cdot(sqrt3 + sqrt2 + sqrt5)}`
`= {(sqrt3 + sqrt2 + sqrt5) - (sqrt3 + sqrt2 - sqrt5)}/{[(sqrt3 + sqrt2) - sqrt5]cdot[(sqrt3 + sqrt2) + sqrt5]}`
`= {sqrt3 + sqrt2 + sqrt5 - sqrt3 - sqrt2 + sqrt5}/{(sqrt3 + sqrt2)^2 - (sqrt5)^2}`
`= {(sqrt5 + sqrt5) + (sqrt3 - sqrt3) + (sqrt2 - sqrt2)}/{3 + 2sqrt6 + 2 - 5}`
`= {2sqrt5}/{(3 + 2 - 5) + 2sqrt6}`
`= {2sqrt5}/{2sqrt6}`
`= {sqrt5}/{sqrt6}`
`= {sqrt5cdot sqrt6}/{sqrt6cdot sqrt6}`
`= {sqrt30}/{6}`
d) `(1 + {5 - sqrt5}/{1 - sqrt5})cdot({5 + sqrt5}/{1 + sqrt5} + 1)`
`= (1 + {sqrt5cdot(sqrt5 - 1)}/{1 - sqrt5})cdot(1 + {sqrt5cdot(sqrt5 + 1)}/{1 + sqrt5})`
`= (1 - {sqrt5cdot(1 - sqrt5)}/{1 - sqrt5})cdot(1 + {sqrt5cdot(1 + sqrt5)}/{1 + sqrt5})`
`= (1 - sqrt5)cdot(1 + sqrt5)`
`= 1^2 - (sqrt5)^2`
`= 1 - 5`
`= - 4`
Đáp án:
a) `= 2sqrt3`
b) `= - 3`
c) `= {sqrt30}/{6}`
d) `= - 4`
