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in Complex number and Quadratic equations by (52.7k points)

If equation x3 - x + a2 - a + 2/3√3 < 0 is true for at least one positive x, then a belongs to

(A)  (0, 1)

(B)  (1, ∞)

(C) (2, 3√3) 

(D)  None of these

1 Answer

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Best answer

Correct option  (B)  (0, 1) 

x3 − x < − a2 + a - 2/3√3

f(x) = x3 − x 

f ′(x) = 3x2 − 1 = 0

⇒ x = ±1/√3

In positive region, minimum value of f(x) 

= 1/3√3 - 1/√3 = -2/3√3

So, 

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