2

Let the solution set of the following system of two inequations

$$x^2 - 4 x + 3 < 0 \\ x^2 - 6 x + 8 < 0$$

be a subset of the solution set of

$$2 x^2 - 9 x + a < 0.$$

How can I find the range of parameter $a$?

I have calculated both solution sets as follows:

Reduce[{x^2 - 4 x + 3 < 0, x^2 - 6 x + 8 < 0}, x]
(* 2 < x < 3 *)

Reduce[2 x^2 - 9 x + a < 0, x]
(* a < 81/8 && 9/4 - 1/4 Sqrt[81 - 8 a] < x < 9/4 + 1/4 Sqrt[81 - 8 a] *)
Domen
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csn899
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1 Answers1

4

Making use of quantifiers, one obtains

ForAll[x, Implies[x^2 - 4 x + 3 < 0 && x^2 - 6 x + 8 < 0, 
2 x^2 - 9 x + a < 0]];
Resolve[%, Reals]

a <= 9

This differs from the Syed's result.

user64494
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