Question

当m为何值时x^2-y^2-x-5y+m可分解为两个一次因式的积

Answer 1

x^2-y^2-x-5y+m

=(x²-x+1/4)-(y²+5y+25/4)-1/4+25/4+m

=(x-1/2)²-(y+5/2)²+m+6

=(x-1/2+y+5/2)(x-1/2-y-5/2)+m+6

=(x+y-2)(x-y-3)+m+6

当m+6=0,即m=-6时,可分解为两个一次因式的积