Question

(x+p)(x+q)=x的平方+mx+36,pq为正整数,求m的值

Answer 1

(x+p)(x+q)=x^2+mx+36

x^2+(p+q)x+pq=x^2+mx+36

p+q=m pq=36

p,q为正整数

p=2,q=18; p=3,q=12; p=4,q=9;p=6,q=6;p=1, q=36;

q=2,p=18; q=3,p=12; q=4,p=9;q=1,p=36.

p+q= 20, 15, 13, 12, 37.

m= 20, 15, 13, 12, 37.