Question

如果4X^3+9X^2+MX+N能被(X+3)(X-1)整除,求M的N次幂

Answer 1

设4x³+9x²+mx+n=A(x+3)(x-1)
x=-3,x+3=0
所以右边等于0
则左边也等于0
x=-3
左边=-108+81-3m+n=0
3m-n=-27 (1)

同理x=1时左边等于0
所以4+9+m+n=0
m+n=-13 (2)
(1)+(2)
4m=-40
m=-10
n=-13-m=-3

Answer 2

f(cosx)
=f[sin(π/2-x)]
=1+cos2(π/2-x)
=1+sin2x
180°-23°17′57〃
=179°59′60〃-23°17′57〃
=(179-23)°(59-17)′(60-57)〃
=156°42′3〃