Hướng dẫn trả lời:
1)
a) `A = (2sqrt{3} - 5sqrt{27} + 4sqrt{12}) ÷ sqrt{3}`
`= (2sqrt{3} - 5sqrt{9*3} + 4sqrt{4*3}) ÷ sqrt{3}`
`= (2sqrt{3} - 5sqrt{3^2*3} + 4sqrt{2^2*3}) ÷ sqrt{3}`
`= (2sqrt{3} - 5*3sqrt{3} + 4*2sqrt{3}) ÷ sqrt{3}`
`= (2sqrt{3} - 15sqrt{3} + 8sqrt{3}) ÷ sqrt{3}`
`= - 5sqrt{3} ÷ sqrt{3}`
`= -5`
b) `B = sqrt{(sqrt{5} - sqrt{2})^2} + sqrt{20} + 1/2sqrt{8}`
`= |sqrt{5} - sqrt{2}| + sqrt{4*5} + 1/2sqrt{4*2}`
`= (sqrt{5} - sqrt{2}) + sqrt{2^2*5} + 1/2sqrt{2^2*2}` (Vì `sqrt{5} > sqrt{2}`)
`= sqrt{5} - sqrt{2} + 2sqrt{5} + 1/2*2sqrt{2}`
`= sqrt{5} - sqrt{2} + 2sqrt{5} + sqrt{2}`
`= (sqrt{5} + 2sqrt{5}) + (- sqrt{2} + sqrt{2})`
`= 3sqrt{5}`
2)
a) `sqrt{x^2 - 10x + 25} = 2`
`↔ sqrt{x^2 - 2*x*5 + 5^2} = 2`
`↔ sqrt{(x - 5)^2} = 2`
`↔ |x - 5| = 2`
`↔ [(x - 5 = 2), (x - 5 = -2):}`
`↔ [(x = 2 + 5), (x = -2 + 5):}`
`↔ [(x = 7), (x = 3):}`
Vậy `x = 7` hoặc `x = 3`
b) `sqrt{9x + 18} - 5sqrt{x + 2} + 4/5sqrt{25x + 50} = 6` (ĐK: `x ≥ -2`)
`↔ sqrt{9*(x + 2)} - 5sqrt{x + 2} + 4/5sqrt{25*(x + 2)} = 6`
`↔ sqrt{3^2*(x + 2)} - 5sqrt{x + 2} + 4/5sqrt{5^2*(x + 2)} = 6`
`↔ 3sqrt{x + 2} - 5sqrt{x + 2} + 4/5*5sqrt{x + 2} = 6`
`↔ 3sqrt{x + 2} - 5sqrt{x + 2} + 4sqrt{x + 2} = 6`
`↔ 2sqrt{x + 2} = 6`
`↔ sqrt{x + 2} = 3`
`↔ {(3 > 0), ((sqrt{x + 2})^2 = 3^2):}`
`↔ x + 2 = 9`
`↔ x = 9 - 2`
`↔ x = 7` (TMĐK)
Vậy `x = 7`
