Here is an attempt to solve the inequality $x ^ { 4 } - 2 x ^ { 2 } - 3 < 0$ by completing the square: $$x ^ { 4 } - 2 x ^ { 2 } - 3 < 0$$ I if and only if $x ^ { 4 } - 2 x ^ { 2 } + 1 < 4$ II if and only if $\left( x ^ { 2 } - 1 \right) ^ { 2 } < 4$ III if and only if $- 2 < x ^ { 2 } - 1 < 2$ IV if and only if $x ^ { 2 } - 1 < 2$ V if and only if $x ^ { 2 } < 3$ VI if and only if $- \sqrt { 3 } < x < \sqrt { 3 }$ Which of the following statements is true? A The argument is completely correct. B The first error occurs in line I. C The first error occurs in line II. D The first error occurs in line III. E The first error occurs in line IV. F The first error occurs in line V. G The first error occurs in line VI.
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Here is an attempt to solve the inequality $x ^ { 4 } - 2 x ^ { 2 } - 3 < 0$ by completing the square:
$$x ^ { 4 } - 2 x ^ { 2 } - 3 < 0$$
I if and only if $x ^ { 4 } - 2 x ^ { 2 } + 1 < 4$
II if and only if $\left( x ^ { 2 } - 1 \right) ^ { 2 } < 4$
III if and only if $- 2 < x ^ { 2 } - 1 < 2$
IV if and only if $x ^ { 2 } - 1 < 2$
V if and only if $x ^ { 2 } < 3$
VI if and only if $- \sqrt { 3 } < x < \sqrt { 3 }$
Which of the following statements is true?
A The argument is completely correct.
B The first error occurs in line I.
C The first error occurs in line II.
D The first error occurs in line III.
E The first error occurs in line IV.
F The first error occurs in line V.
G The first error occurs in line VI.