Toán Lớp 8: Cho a+b+c=0. Chứng minh a^3+b^3-c^3=-3abc
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Toán Lớp 8: Cho a+b+c=0. Chứng minh a^3+b^3-c^3=-3abc
Comments ( 2 )
⇒ (a+b+c)³=0
⇒ a³+b³+c³+3a²b+3ab²+3b²c+3bc²+3a²c+3ac²+6abc=0
⇒ a³+b³+c³+(3a²b+3ab²+3abc)+(3b²c+3bc²+3abc)+(3a²c+3ac²+3abc)-3abc=0
⇒ a³+b³+c³+3ab(a+b+c)+3bc(a+b+c)+3ac(a+b+c)=3abc
⇒ a³+b³+c³+3ab.0+3bc.0+3ac.0=3abc
⇒ a³+b³+c³=3abc
Vậy a³+b³+c³=3abc khi a+b+c=0