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Bài `4:`

`a)`

`A= {3sqrt4 -14 - ( sqrtx +3 )(sqrtx -3) + (2sqrtx -1)(sqrtx -2)}/{(sqrtx -2)(sqrtx -3)}`

`= { 3sqrtx -14 - x+9 + 2x -sqrtx - 4sqrtx +2}/{(sqrtx -2)(sqrtx -3)}`

`= { -2sqrtx + x -3}/{(sqrtx -2)(sqrtx -3)}`

`={(sqrtx -3 )(sqrtx +1)}/{(sqrtx -2)(sqrtx -3)}`

`={ sqrtx -1}/{sqrtx -2}`

Ta có:

`x=7-4sqrt3 = 4 - 2.2sqrt3 +3 = (2-sqrt3)^2`

`=> sqrtx = 2-sqrt3`

`=> A= { 2-sqrt3 +1}/{ 2-sqrt3 -2}`

`={3 -sqrt3}/{ -sqrt3}`

`={ sqrt3 .( sqrt3 -1)}/{ -sqrt3}`

`=1 - sqrt3`

`b)`

Để `A>1`

`=> {sqrtx -1}/{sqrtx -2} >1`

`=>  {sqrtx -1}/{sqrtx -2} -1 >0`

`=> { sqrtx -1 -  sqrtx +2}/{ sqrtx -2} > 0`

`=> 3/{sqrtx -2} > 0`

`=> sqrtx -2 >0`

`=> sqrtx > 2`

`=> x > 4`