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

Toán Lớp 9: Tính: a) 2/(1-√2) + (6+2√2)/(3+√2) b) 1/(1-√2+√3)-1/(1-√2-√3)

Tháng Mười Hai 13, 2022 Toán học 1 Comment 0 views

Toán Lớp 9: Tính:
a) 2/(1-√2) + (6+2√2)/(3+√2)
b) 1/(1-√2+√3)-1/(1-√2-√3)

Comments ( 1 )

  1. minhtamnguyet88
    minhtamnguyet88
    13 Tháng Mười Hai, 2022 at 9:32 sáng
    Reply
    a) 
    2/(1-sqrt2) + (6+2sqrt2)/(3+sqrt2)
    = (2(1+sqrt2))/((1-sqrt2)(1+sqrt2)) + ((6+2sqrt2)(3-sqrt2))/((3+sqrt2)(3-sqrt2))
    = (2(1+sqrt2))/(1^2 – (sqrt2)^2) + ((6+2sqrt2)(3-sqrt2))/(3^2 – (sqrt2)^2)
    = -2(1+sqrt2) + (18-6sqrt2+6sqrt2-4)/7
    = -2 – 2sqrt2 + 14/7
    = -2 – 2sqrt2 + 2
    = -2sqrt2
    b)
    1/(1-sqrt2+sqrt3) – 1/(1-sqrt2-sqrt3)
    = (1(1-sqrt2-sqrt3))/((1-sqrt2+sqrt3)(1-sqrt2-sqrt3)) – (1(1-sqrt2+sqrt3))/((1-sqrt2-sqrt3)(1-sqrt2+sqrt3))
    = (1-sqrt2-sqrt3)/((1-sqrt2)^2-sqrt3^2) – (1-sqrt2+sqrt3)/((1-sqrt2)^2-sqrt3^2)
    = (1-sqrt2-sqrt3)/(-2sqrt2) – (1-sqrt2+sqrt3)/(-2sqrt2)
    = -((1-sqrt2-sqrt3)sqrt2)/4 + ((1-sqrt2+sqrt3)sqrt2)/4
    = -(sqrt2-2-sqrt6)/4 + (sqrt2-2+sqrt6)/4
    = (-(sqrt2-2sqrt6)+sqrt2-2+sqrt6)/4
    = (-sqrt2+2+sqrt6+sqrt2-2+sqrt6)/4
    = (2sqrt6)/4
    = sqrt6/2

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

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