p-x-x-3-3ax-2-3a-2-1-x-a-3-a-p-2-lt-0-prove-that-2-lt-a-lt-3-

Question Number 157184 by cortano last updated on 20/Oct/21

p (x) = x^{3} - 3 {a x}^{2} + (3 a^{2} + 1) x - (a^{3} + a)

p (2) < 0

p r o v e t h a t 2 < a < 3

Answered by ghimisi last updated on 20/Oct/21

p (x) = x^{3} - 3 {a x}^{2} + 3 a^{2} x - x^{3} + x - a = {(x - a)}^{3} + x - a

p (2) < 0 \Rightarrow (2 - a) [{(2 - a)}^{2} + 1] < 0 \Rightarrow a > 2

a < 3 ? ? ? ? ? ?

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