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If a ≠ b ≠ c, prove that (a, a2), (b, b2), (0, 0) will not be collinear.

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Let A (a, a2), B (b, b2) and C (0, 0) are the vertices of a triangle.

Let us assume that that points are collinear, then area of ∆ABC must be zero.

Now, area of ∆ABC

Which is contraction to our assumption.

This implies points are not be collinear. Hence proved.

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