请数学高手进f(x)=ax^3+bx^2+cx+d,g(x)=x^3+2x^2+3x+1拜托各位大神

问题描述:

请数学高手进f(x)=ax^3+bx^2+cx+d,g(x)=x^3+2x^2+3x+1拜托各位大神
(1),若F(x)=f(x)-g(x)是偶函数,求abcd的值 (2)若H(x)=f(x)+g(x)是奇函数,求abcd的值

F(x)=f(x)-g(x)=(a-1)x^3+(b-2)x^2+(c-3)x+d-1 F(x)是偶函数,所以F(-x)=F(x) -(a-1)x^3+(b-2)x^2-(c-3)x+d-1=(a-1)x^3+(b-2)x^2+(c-3)x+d-1 2(a-1)x^3+2(c-3)x=0,因为x是变量所以,2(a-1)=2(c-3)=0,解得a=1,c=3 若H(x)=f(x)+g(x)是奇函数 H(x)=(a+1)x^3+(b+2)x^2+(c+3)x+d+1 H(-x)=-(a+1)x^3+(b+2)x^2-(c+3)x+d+1 -[(a+1)x^3+(b+2)x^2+(c+3)x+d+1]=-(a+1)x^3+(b+2)x^2-(c+3)x+d+1 2(b+2)x^2+2(d+1)=0,因为x是变量所以,2(b+2)=2(d+1),解得b=-2,d=-1 abcd=1*(-2)*3*(-1)=6 题目是这个意思吗?