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

Toán Lớp 8: Chung minh (a^2+b^2)(c^2+d^2)=(ac+bd)^2+(ad-bc)^2

Toán Lớp 8: Chung minh
(a^2+b^2)(c^2+d^2)=(ac+bd)^2+(ad-bc)^2

Comments ( 2 )

  1. (a^2+b^2)(c^2+d^2)=(ac+bd)^2+(ad-bc)^2
    ->a^2c^2+a^2d^2+b^2c^2+b^2d^2=a^2c^2+2abcd+b^2d^2+a^2d^2-2abcd+b^2c^2
    ->a^2c^2+a^2d^2+b^2c^2+b^2d^2-a^2c^2-b^2d^2-a^2d^2-b^2c^2=2abcd-2abcd
    ->0=0
    ->(TM)
     

  2.     (a²+b²)(c²+d²)=(ac+bd)²+(ad-bc)²
    ⇔ a²c²+a²d²+b²c²+b²d²=a²c²+2acbd+b²d²+a²d²-2abcd+b²c²
    ⇔ a²c²+a²d²+b²c²+b²d²=a²c²+b²d²+a²d²+b²c²
    ⇒ đpcm
    .-. 
     

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

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