(1)(x+4)(x+9)=x^2+mx+36
x^2+13x+36=x^2+mx+36
m=13
(2)(x-2)(x-18)=x^2+mx+36
x^2-20x+36=x^2+mx+36
m=-20
(3)(x+3)(x+p)=x^2+mx+36
x^2+(3+p)x+3p=x^2+mx+36
3+p=m
3p=36
解得:
p=12
m=15
(4)(x-6)(x-p)=x^2mx+36
x^2-(6+p)x+6p=x^2+mx+36
6+p=-m
6p=36
解得:
p=6
m=-12
(5)(x+p)(x+q)=x^2+mx+36,p,q为正整数
x^2+(p+q)x+pq=x^2+mx+36
qp=36
p+q=m
p,q为正整数,
所以
1)p,q分别为1,36,m=37
2)p,q分别为2,18,m=20
3)p,q分别为3,12,m=15
4)p,q分别为4,9,m=13
5)p,q分别为6,6,m=12