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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 9: Rút gọn biểu thức 2/√3-1 + 1/√3 – √27

Toán Lớp 9: Rút gọn biểu thức
2/√3-1 + 1/√3 – √27

Comments ( 2 )

  1. Hướng dẫn trả lời:
    {2}/{sqrt{3} – 1} + {1}/{sqrt{3}} – sqrt{27}
    = {2cdot(sqrt{3} + 1)}/{(sqrt{3} – 1)cdot(sqrt{3} + 1)} + {1}/{sqrt{3}} – sqrt{3^3}
    = {2cdot(sqrt{3} + 1)}/{(sqrt{3})^2 – 1^2} + {1}/{sqrt{3}} – 3sqrt{3}
    = {2cdot(sqrt{3} + 1)}/{3 – 1} + {1}/{sqrt{3}} – 3sqrt{3}
    = {2cdot(sqrt{3} + 1)}/{2} + {1}/{sqrt{3}} – 3sqrt{3}
    = (sqrt{3} + 1) + {1}/{sqrt{3}} – 3sqrt{3}
    = {3cdot(sqrt{3} + 1)}/{3} + {sqrt{3}}/{(sqrt{3})^2} – {3cdot sqrt{3}}/(sqrt3)^2
    = {3sqrt{3} + 3}/{3} + {sqrt{3}}/{3} – {9sqrt{3}}/3
    = {3sqrt{3} + 3 + sqrt{3} – 9sqrt{3}}/3
    = {3 + (3sqrt{3} + sqrt{3} – 9sqrt{3})}/3
    = {3 – 5sqrt{3}}/3
    Giải đáp:
    = {3 – 5sqrt{3}}/3

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222-9+11+12:2*14+14 = ? ( )