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

Toán Lớp 8: cho x + y + z = 0. CMR x^3 + y^3 + z^3 = 3xyz

Toán Lớp 8: cho x + y + z = 0. CMR x^3 + y^3 + z^3 = 3xyz

Comments ( 1 )

  1. Ta có:
    $x^{3}+$ $y^{3}+$ $z^{3}-3xyz=(x+y)^3-3x^2y-3xy^2+z^3-3xyz$ 
    $=(x+y)^{3}+z^3-3xy(x+y+z)$ 
    $=(x+y+z)($ ($x+y)^{2}-z(x+y)+z^2)-3xy(x+y+z)$ 
    $=(x+y+z)$($x^{2}+2xy+y^2-zx-yz-3xy)=0$ vì x+y+z=0
    Vì x³+y³+z³-3xyz=0 nên x³+y³+z³=3xyz

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

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