设y=kx,是否存在实数k使代数式(x^2-y^2)(4x^2-y^2)+3x^2(4x^2-y2)能化简为x^4?

设y=kx,是否存在实数k使代数式(x^2-y^2)(4x^2-y^2)+3x^2(4x^2-y2)能化简为x^4?
设y=kx,是否存在实数k使代数式(x^2-y^2)(4x^2-y^2)+3x^2(4x^2-y
2)能化简为x^4?

设y=kx,是否存在实数k使代数式(x^2-y^2)(4x^2-y^2)+3x^2(4x^2-y2)能化简为x^4?
把y=kx代入(x^2-y^2)(4x^2-y^2)+3x^2(4x^2-y^2)=(4x^2-y^2)^2得
[(4-k^2)x^2]^2=x^4,
∴(4-k^2)^2=1,
∴k^2-4=土1,
∴k^2=5,或3,
∴k=土√5或土√3.

这个题目是中考题