Question

已知3x^2-4xy-7y^2+13x-37y+m=0可以分成2个一次因式的乘积求 m

Answer 1

3x^2-4xy-7y^2+13x-37y+m=0

(3x-7y)(x+y)+13x-37y+m=0

则有(3x-7y+a)(x+y+b)=0

所以(3x-7y)(x+y)+a(x+y)+b(3x-7y)+ab=0

(3x-7y)(x+y)+(a+3b)x+(a-7b)y+ab=0

(3x-7y)(x+y)+13x-37y+m=0

所以a+3b=13

a-7b=-37

且m=ab

解得b=5,a=-2

所以m=ab=-10