Question Bank - General Aptitude

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If x is real and |??2 ? 2?? + 3| = 11, then possible values of | ? ??3 + ??2 ? ??| include

A.
2, 4
B.
2, 14
C.
4, 52
D.
14, 52

Solution:

|??2 ? 2?? + 3| = 11??2 ? 2?? + 3 = 11 or ??2 ? 2?? + 3 = -11By taking: ??2 ? 2?? + 3 = 11??2 ? 2?? ? 8 = 0??2 ? 4?? + 2?? ? 8 = 0??(?? - 4) + 2(?? ? 4) = 0(?? + 2)(?? ? 4) = 0?? = ?2 or ?? = 4Substitute: ?? = -2|? ??3 + ??2 ? ??| = | ? (?2)3 + (?2)2 ? (?2)| = |14 | = 14Substitute: ?? = 4|? ??3 + ??2 ? ??| = | ? 43 + 42 ? 4| = |-52 | = 52The possible values of | ? ??3 + ??2 ? ??| include 14 and 52

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