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

Question

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

Answer 1

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（...