Let t be a real number, f (x) = x + T / x2 + 1, if x belongs to [- 1,2], then the inequality f (x)

The inequality is reduced to:
2tx^2-x+t>=0
Let y = 2tx ^ 2-x + t
When t = 0, y = - x cannot always be greater than 0, so it does not hold
So t is not equal to 0
Axis of symmetry equation x = 1 / 2T
When 1 / 2t2, 0 = 2 / 9
When - 1 = 1 / 4
To sum up: T > = 1 / 4

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