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Official 2023 Paper 2 · Q10

Paper 2Logic & proofGeometryAlgebra

Here is an attempt to solve the inequality x4−2x2−3<0x^4-2x^2-3<0 by completing the square:

x4−2x2−3<0x^4-2x^2-3<0
  • I. if and only if x4−2x2+1<4x^4-2x^2+1<4
  • II. if and only if (x2−1)2<4(x^2-1)^2<4
  • III. if and only if −2<x2−1<2-2<x^2-1<2
  • IV. if and only if x2−1<2x^2-1<2
  • V. if and only if x2<3x^2<3
  • VI. if and only if −3<x<3-\sqrt3<x<\sqrt3

Which of the following statements is true?

AThe argument is completely correct.
BThe first error occurs in line I.
CThe first error occurs in line II.
DThe first error occurs in line III.
EThe first error occurs in line IV.
FThe first error occurs in line V.
GThe first error occurs in line VI.

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