Question

1, cho a+b+c=0
CMR: a³+b³+c³=3abc
2, cho a+b-c=0
CMR: a³+b³-c³=-3abc

Answer 1

1) Có: \(a+b+c=0\)

\(\Leftrightarrow a+b=-c\)

\(\Leftrightarrow\left(a+b\right)^3=-c^3\)

\(\Leftrightarrow a^3+b^3+3ab\left(a+b\right)=-c^3\)

\(\Leftrightarrow a^3+b^3-3abc=-c^3\)

\(\Leftrightarrow a^3+b^3+c^3=3abc\)

2)Có: \(a+b-c=0\)

\(\Leftrightarrow a+b=c\)

\(\Leftrightarrow\left(a+b\right)^3=c^3\)

\(\Leftrightarrow a^3+b^3+3ab\left(a+b\right)=c^3\)

\(\Leftrightarrow a^3+b^3+3abc=c^3\)

\(\Leftrightarrow a^3+b^3-c^3=-3abc\)