If a≠b≠0, prove that the points ( a, a^2),( b, b^2) (0, 0)
will not be collinear.
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It is given that a isn't equal to b not equal to 0
Area of these points=1/2 {x1(y2-y3)+x2(y3-y1)+x3(y1-y2)}
1/2 {a(b^2-0)+b(0-a^2)+0(a^2-b^2)}
1/2 {ab^2-a^2b+0}
1/2{ab(b-a)}
But a and b are not equal to 0
Hence area of these points is not equal to 0
And the points are not collinear
Area of these points=1/2 {x1(y2-y3)+x2(y3-y1)+x3(y1-y2)}
1/2 {a(b^2-0)+b(0-a^2)+0(a^2-b^2)}
1/2 {ab^2-a^2b+0}
1/2{ab(b-a)}
But a and b are not equal to 0
Hence area of these points is not equal to 0
And the points are not collinear
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