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Family of lines x (a + b) + y = 1 where ...

Family of lines `x (a + b) + y = 1` where `a and b` are roots of the equation `x^3 - 3x^2 + x + lambda = 0 and [a + b] = 1` (where [.] denotes the greatest integer function) such that it intercepts a triangle of area A with coordinate axes,then `A_max` is

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