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确定下列各式中m的值.(1)(x+4)(x+9)=x2+mx+36;(2)(x-2)(x-18)=x2+mx+36;(3)(x+3)(x+p)=x2+mx+36;(4)(x-6)(x-p)=x2+mx+36;(5)(x+p)(x+q)=x2+mx+36,p、q为正整数.

题目详情
确定下列各式中m的值.
(1)(x+4)(x+9)=x2+mx+36;
(2)(x-2)(x-18)=x2+mx+36;
(3)(x+3)(x+p)=x2+mx+36;
(4)(x-6)(x-p)=x2+mx+36;
(5)(x+p)(x+q)=x2+mx+36,p、q为正整数.
▼优质解答
答案和解析
(1)(x+4)(x+9)=x2+13x+36=x2+mx+36,
解得:m=13;
(2)(x-2)(x-18)=x2-20x+36=x2+mx+36,
解得:m=-20;
(3)(x+3)(x+p)=x2+(p+3)x+3p=x2+mx+36,
∴p+3=m,3p=36,
解得:m=15,p=12;
(4)(x-6)(x-p)=x2-(p+6)x+6p=x2+mx+36,
∴-p-6=m,6p=36,
解得:m=-12,p=6;
(5)(x+p)(x+q)=x2+(p+q)x+pq=x2+mx+36,p、q为正整数,
∴p+q=m,pq=36,
当p=1,q=36时,m=37;当p=2,q=18时,m=20;当p=3,q=12时,m=15;当p=4,q=9时,m=13,当p=q=6时,p+q=12,
综上,m的值为37,20,15,13,12.