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Updated on: 03 Jun 2021, 01:23
Originally posted by Skywalker18 on 19 Jun 2016, 11:13.
Last edited by Bunuel on 03 Jun 2021, 01:23, edited 3 times in total.
Last edited by Bunuel on 03 Jun 2021, 01:23, edited 3 times in total.
Renamed the topic and edited the question.
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E
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If |x| < x^2, which of the following must be true ?
A. x > 0
B. x < 0
C. x > 1
D. -1 < x < 1
E. x^2 > 1
A. x > 0
B. x < 0
C. x > 1
D. -1 < x < 1
E. x^2 > 1
21 Jun 2016, 22:12
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Skywalker18
If |x| < x^2, which of the following must be true ?
A. x > 0
B. x < 0
C. x > 1
D. -1 < x < 1
E. x^2 > 1
A. x > 0
B. x < 0
C. x > 1
D. -1 < x < 1
E. x^2 > 1
|x| < x^2
Both left hand side and Right Hand side are positive, so we can square the inequalities.
\(x^2 < x^4\)
\(x^4 > x^2\)
\(x^4 - x^2 > 0\)
\(x^2(x^2 - 1)> 0\)
x^2 is always positive.
So the condition is
\(x^2 - 1> 0\)
\(x^2 > 1\)
E is the answer.
19 Jun 2016, 11:20
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Skywalker18
If |x| < x^2, which of the following must be true ?
A. x > 0
B. x < 0
C. x > 1
D. -1 < x < 1
E. x^2 > 1
A. x > 0
B. x < 0
C. x > 1
D. -1 < x < 1
E. x^2 > 1
Given: \(|x|<x^2\) --> reduce by \(|x|\) (side note: we can safely do this as absolute value is non-negative and in this case we know it's not zero too, as if x would be zero inequality wouldn't hold true, so \(|x|>0\)) --> \(1<|x|\) --> \(x<-1\) or \(x>1\).
So we have that \(x<-1\) or \(x>1\).
A. x > 0. Not always true.
B. x < 0. Not always true.
C. x > 1. Not always true.
D. -1 < x < 1. Not true.
E. x^2 > 1. Always true.
Answer: E.
To understand the underline concept better practice other Trickiest Inequality Questions Type: Confusing Ranges.
Hope it helps.
i have just one question
