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

Toán Lớp 9: Tính: a) (√5 + 2) × ((√5 + 2)² – 8√5)/(√5 – 2) b) ((1- √2)/(1 + √2) – (1 + √2)/(1- √2)) : √72

Toán Lớp 9: Tính: a) (√5 + 2) × ((√5 + 2)² – 8√5)/(√5 – 2)
b) ((1- √2)/(1 + √2) – (1 + √2)/(1- √2)) : √72

Comments ( 1 )

  1. Giải đáp:
     
    Lời giải và giải thích chi tiết:
    a)
    (sqrt5+2)((sqrt5+2)^2-8sqrt5)/(sqrt5-2)
    = (sqrt5+2)(9+4sqrt5-8sqrt5)/(sqrt5-2)
    = (sqrt5+2)(9-4sqrt5)/(sqrt5-2)
    = ((9-4sqrt5)(sqrt5+2))/(sqrt5-2)
    = (9sqrt5+9*2-4sqrt5sqrt5-4*2sqrt5)/(sqrt5-2)
    = (sqrt5-2)/(sqrt5-2)
    = 1
    b) 
    ((1-sqrt2)/(1+sqrt2) – (1+sqrt2)/(1-sqrt2)) \div sqrt{72}
    = -((1-sqrt2)^2-(1+sqrt2)^2)/((1+sqrt2)(1-sqrt2)) \div 6sqrt2
    = -(3+2sqrt2-3+2sqrt2)/(1^2-(sqrt2)^2)
    = -(4sqrt2)/(-1)
    = 4sqrt2 \div 6sqrt2
    = 2/3

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

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