Solve equation xy^2-(3x^2-4x+1)y+x^3-2x^2+x=0, in \mathbb{R}.

NepanitaNesg3a

NepanitaNesg3a

Answered question

2022-04-20

Solve equation xy2(3x24x+1)y+x32x2+x=0, in R.

Answer & Explanation

Elliot Roy

Elliot Roy

Beginner2022-04-21Added 14 answers

Not sure why you put y=ax, since this is clearly a quadratic equation in y:
xy2(3x24x+1)y+x32x2+x=0
Its discriminant is
D=(3x1)2(x1)24x2(x1)2=(x1)3(5x1)
So y is defined for x(-,15][1,) and x0:
y=(x-1)(3x-1±(x-1)(5x-1))2x

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