1.

Show that the three distinct points (a^2,a) (b^2,b) and (c^2,c) can never be collinear.

Answer»

Solution :Area of triangle with VERTICES `(a^2,a) (b^2,b)` and `(c^2,c)` is
`1/2 {a^2(b-c) + b^2(c-a) + c^2(a-b)}`
= (a-b) (b-c) (a-c)
which is NEVER equal to ZERO except when a = b = c, hence the points are not collinear.


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