Hướng dẫn trả lời:
Câu 25:
a) `A = sqrt8 - sqrt32 + sqrt50`
`= sqrt{2^2cdot2} - sqrt{4^2cdot2} + sqrt{5^2cdot2}`
`= 2sqrt{2} - 4sqrt{2} + 5sqrt{2}`
`= 3sqrt2`
b) `B = (3 + {a + sqrta}/{sqrta + 1})cdot(3 - {a - sqrta}/{sqrta - 1})` `(a ≥ 0; a ne 1)`
`= (3 + {sqrtacdot(sqrta + 1)}/{sqrta + 1})cdot(3 - {sqrtacdot(sqrta - 1)}/{sqrta - 1})`
`= (3 + sqrta)cdot(3 - sqrta)`
`= 3^2 - (sqrta)^2`
`= 9 - a`
Câu 26:
a) `A = 2/{2 - sqrt3} - sqrt12 + sqrt18/sqrt2`
`= 2/{2 - sqrt3} - 2sqrt3 + {3sqrt2}/sqrt2`
`= 2/{2 - sqrt3} - 2sqrt3 + 3`
`= 2/{2 - sqrt3} - {2sqrt3cdot(2 - sqrt3)}/{2 - sqrt3} + 3`
`= {2 - 2sqrt3cdot(2 - sqrt3)}/{2 - sqrt3} + 3`
`= {2 - 4sqrt3 + 6}/{2 - sqrt3} + 3`
`= {8 - 4sqrt3}/{2 - sqrt3} + 3`
`= {4cdot(2 - sqrt3)}/{2 - sqrt3} + 3`
`= 4 + 3`
`= 7`
b) `B = {a + 3sqrta}/{a - 9} - {3sqrta}/{a - 3sqrta}`
`= {a + 3sqrta}/{(sqrta)^2 - 3^2} - {3sqrta}/{a - 3sqrta}`
`= {sqrtacdot(sqrta + 3)}/{(sqrta - 3)cdot(sqrta + 3)} - {3sqrta}/{sqrtacdot(sqrta - 3)}`
`= {sqrta}/{sqrta - 3} - {3}/{sqrta - 3}`
`= {sqrta - 3}/{sqrta - 3}`
`= 1`
Câu 27:
a) `2sqrt16 - sqrt25`
`= 2sqrt{4^2} - sqrt{5^2}`
`= 2cdot4 - 5`
`= 8 - 5`
`= 3`
