与木有关的字:又是不等式

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当x<=1时
求证:x^3+3x^2<=4

x^3+3x^2<=4
即x^3-1+3x^2-3<=0
即(x-1)(x^2+x+1)+3(x-1)(x+1)<=0
即(x-1)(x^2+4x+4)<=0
x<=1
x-1<=0
x^2+4x+4>=0
得证

1,x<=1 =>
x^3<=1

2, x<=1 => x^2 <=1 => 3x^2 <= 3

1,2 => x^3 + 3x^2 <= 4