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The curve [itex]y=x^4-2x^3-2x^2-2x[/itex] has a bitangent. I need to find the equation of this line.

First, I started off by computing the slope. Since it touches two points on the curve, their slopes should be the same.

So, I have the equation [itex]4x^3_1-6x^2_1-4x_1-2=4x^3_2-6x^2_2-4x_2-2[/itex]

I got up to the point where I have [itex]x^2_1+x_1x_2+x^2_2 = 3/2(x_1+x_2) + 1[/itex]

I seem to be stuck here. Any help?

First, I started off by computing the slope. Since it touches two points on the curve, their slopes should be the same.

So, I have the equation [itex]4x^3_1-6x^2_1-4x_1-2=4x^3_2-6x^2_2-4x_2-2[/itex]

I got up to the point where I have [itex]x^2_1+x_1x_2+x^2_2 = 3/2(x_1+x_2) + 1[/itex]

I seem to be stuck here. Any help?

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