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29 Mar 2021, 05:30
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
91% (01:14) correct
9%
(01:43)
wrong
based on 395
sessions
History
Date
Time
Result
Not Attempted Yet
Given the equation \(|x^2-2|>1\), which of the following could not be a value of x?
A. –1
B. –2
C. –3
D. –4
E. –5
A. –1
B. –2
C. –3
D. –4
E. –5
29 Mar 2021, 07:26
Kudos
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Bunuel
Substitute the options in the given inequality
\(|x^2-2|>1\)
1) x=-1...... \(|(-1)^2-2|>1......|1-2|>1.......1>1\)....No
OR we can solve the inequality
\(|x^2-2|>1\)
If \(x^2\geq 2\), then \(x^2-2>1......x^2>3\).....\(-\sqrt{3}>x...........x>\sqrt{3}\)
If \(x^2\leq 2\), then \(2-x^2>1......x^2<1.........-1<x<1\)
B, C, D and E fall in \(x<-\sqrt{3}\)
A
31 Mar 2021, 07:54
Kudos
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Solution
Given
We are given that:
- • |\(x^2\)−2| > 1
To find
We need to determine
- • The choice that CANNOT be a value of x
Approach and Working out
- • |\(x^2\)−2| > 1
- o This can read in terms of distance as: the distance of \(x^2\) from 2 is greater than 1.
o The distance is equal to 1 at \(x^2\) = 1 and 3.
- So, distance is greater than 1 if \(x^2\) > 3 or \(x^2\) < 1. ------(1)
- • Choice A:
- o x = 1
- So, \(x^2\) = 1.
But 1 is neither greater than 3 nor less than 1.
This value of \(x^2\) does not satisfy equation (1).
• So, x CANNOT be equal to 1
Thus, option A is the correct answer.
Correct Answer: Option A
