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soumya_165
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(1-x^2) >= 0
this can be simplified to x^2<=1
x lies btw -1 to +1 ( -1<= x <= 1 )
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Inequality Problem
Source: Beat The GMAT — Problem Solving |
Your equation can be easily written as following:
x^2 <= 1 or x>=-1 and x<=1, hence x belongs to the segment[-1;1]
x^2 <= 1 or x>=-1 and x<=1, hence x belongs to the segment[-1;1]
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soumya_165
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Thanks Javoni and Shalini for your response.
I had also solved the problem the way u did but I am bit confused with the explanation given in OG 12(this is a problem from OG12). I was expecting some one would solve it that way.
I am mentioning the answer explanation below from OG12 and also underlining the text in which I am confused. Please let me know how it is being derived
"The expression 1-x^2 can be factored as (1-x)(1+x). The product is positive when both the factors are positive (this happens if 1>=x and x>=-1, or equivalently if -1<=x<=1) or both factors are negative (this happens if 1<=x and x <=1, which cannot happen), and therefore the solution is -1<=x<=1"
When both the factors are +ve then the issue will be simplified to -1<=x<=1 but when both the factors are -ve how can it be simplified to 1<=x and x <=1?
I had also solved the problem the way u did but I am bit confused with the explanation given in OG 12(this is a problem from OG12). I was expecting some one would solve it that way.
I am mentioning the answer explanation below from OG12 and also underlining the text in which I am confused. Please let me know how it is being derived
"The expression 1-x^2 can be factored as (1-x)(1+x). The product is positive when both the factors are positive (this happens if 1>=x and x>=-1, or equivalently if -1<=x<=1) or both factors are negative (this happens if 1<=x and x <=1, which cannot happen), and therefore the solution is -1<=x<=1"
When both the factors are +ve then the issue will be simplified to -1<=x<=1 but when both the factors are -ve how can it be simplified to 1<=x and x <=1?
When both factors are negative this implies
"The expression 1-x^2 can be factored as (1-x)(1+x). The product is positive when both the factors are positive (this happens if 1>=x and x>=-1, or equivalently if -1<=x<=1) or both factors are negative (this happens if 1<=x and x <=1, which cannot happen), and therefore the solution is -1<=x<=1"
When both the factors are +ve then the issue will be simplified to -1<=x<=1 but when both the factors are -ve how can it be simplified to 1<=x and x <=1?
A) -(1-x)>= 0 and B) -(1+x)>=0
A becomes 1>= x and B becomes x<=-1
But for these values of x the inequality 1-x^2>=0 does not hold good.
SO we consider both (1-x) and (1+x) to be positive.
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soumya_165
- Newbie | Next Rank: 10 Posts
- Posts: 8
