TMUA 2023 Paper 2 Q10 — Worked Solution

P2·Inequalities·6.5Official · 2023 · Q10

proof-errorcompleting-the-squareinequality

Here is an attempt to solve the inequality

x^{4} - 2 x^{2} - 3 < 0

by completing the square:

if and only if

x^{4} - 2 x^{2} + 1 < 4

if and only if

(x^{2} - 1)^{2} < 4

III

if and only if

- 2 < x^{2} - 1 < 2

if and only if

x^{2} - 1 < 2

if and only if

x^{2} < 3

if and only if

- 3 < x < 3

Which of the following statements is true?

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