解个方程:X^3+2X^2+X+4/27=0

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解个方程:X^3+2X^2+X+4/27=0
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解个方程:X^3+2X^2+X+4/27=0
解个方程:X^3+2X^2+X+4/27=0

解个方程:X^3+2X^2+X+4/27=0
X^3+2X^2+X+4/27=(X^3+1/27)+(2X^2+X+1/9)
=(X+1/3)(X^2-X/3+1/9)+(X+1/3)(2X+1/3)
=(X+1/3)(X^2+5X/3+4/9)
=(X+1/3)(X+1/3)(X+4/3)
=(X+1/3)^2(X+4/3)
∴(X+1/3)^2(X+4/3)=0
X+1/3=0或X+4/3=0
X=-1/3或X=-4/3

X^3+2X^2+X+4/27=(X^3+1/27)+(2X^2+X+1/9)
=(X+1/3)(X^2-X/3+1/9)+(X+1/3)(2X+1/3)
=(X+1/3)^2(X+4/3)=0
X+1/3=0或X+4/3=0
X=-1/3或X=-4/3