Rút gọn 3x - căn bậc hai (x^2 - 2x + 1)
Rút gọn \(3{\rm{x}} - \sqrt {{x^2} - 2{\rm{x}} + 1} \).
Ta có \(3{\rm{x}} - \sqrt {{x^2} - 2{\rm{x}} + 1} = 3{\rm{x}} - \sqrt {{{\left( {x - 1} \right)}^2}} = 3x - \left| {x - 1} \right|\)
+) Nếu x ≥ 1 thì x – 1 ≥ 0
\(3{\rm{x}} - \sqrt {{x^2} - 2{\rm{x}} + 1} = 3{\rm{x}} - x + 1 = 2{\rm{x}} + 1\)
+) Nếu x < 1 thì x – 1 < 0
\(3{\rm{x}} - \sqrt {{x^2} - 2{\rm{x}} + 1} = 3{\rm{x + }}x - 1 = 4{\rm{x }} - 1\)