[toán 9] c/m đẳng thức

E

eye_smile

x+y+z=0 \Rightarrow $-x=y+z$

\Rightarrow $(y+z)^5=-x^5$

\Leftrightarrow $y^5+5y^4z+10y^2z^2+10y^2z^3+5yz^4+z^5=-x^5$

\Leftrightarrow $(x^5+y^5+z^5)+5yz(y^3+2y^2z+2yz^2+z^3)=0$

\Leftrightarrow $(x^5+y^5+z^5)+5yz(y+z)(y^2+yz+z^2)=0$

\Leftrightarrow $2(x^5+y^5+z^5)-5xyz(2y^2+2z^2+2yz)=0$

\Leftrightarrow $2(x^5+y^5+z^5)=5xyz(x^2+y^2+z^2)$
 
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