Question

a.b是有理数x^6＋2ax^3y＋a^2y^2－(a^6x^6+2a^3bx^3y+b^2y^2)结果与单项式ax^3

Answer 1

x^6＋2ax^3y＋a^2y^2－(a^6x^6+2a^3bx^3y+b^2y^2)

=(1-a^6)x^6+(2a-2a^3b)x^3y+(a^2-b^2)y^2

要使这结果与单项式ax^3y是同类项,则必须有

1-a^6=0 (1)

2a-2a^3b=a (2)

a^2-b^2=0 (3)

即a^6=1 (4)

a=2a^3b (5)

a^2=b^2 (6)

由(4)(6)得到b^6=1,即b=1或b=-1

但是将b=1或b=-1分别代入(5)得到a=2a^3,或a=-2a^3

即a^2=(2a^3)^2=4a^6=4

与(6)矛盾

所以无解