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If x^5>x^3
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26 Apr 2024, 00:51
26 Apr 2024, 00:51
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Question Stats:
35% (01:09) correct
64% (01:10) wrong based on 34 sessions
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If \(x^5>x^3\) , then which of the following could be true ?
I. \(x>0\)
II. \(x<0\)
III. \(x<-1\)
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I,II, and III
I. \(x>0\)
II. \(x<0\)
III. \(x<-1\)
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I,II, and III
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Re: If x^5>x^3
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09 May 2024, 09:16
09 May 2024, 09:16
1
I. x > 0
If x is greater than 1 (which is greater than 0), \(x^5\) will be greater than \(x^3\). Thus, (I) could be true.
E.g., if x = 2, \(x^5\) = 32 and \(x^3\) = 8 ---> 32 > 8
II. x < 0
If x is less than 0 but greater than -1, \(x^5\) will be greater than \(x^3\). Thus, (II) could be true.
E.g., if x = -0.5, \(x^5\) = -0.03125 and \(x^3\) = -0.125 ---> -0.03125 > -0.125
III. x < -1
If x is less than -1, \(x^5\) will always be less than \(x^3\). Thus, (III) cannot be true.
E.g., if x = -2, \(x^5\) = -32 and \(x^3\) = -8 ---> -32 < -8
If x is greater than 1 (which is greater than 0), \(x^5\) will be greater than \(x^3\). Thus, (I) could be true.
E.g., if x = 2, \(x^5\) = 32 and \(x^3\) = 8 ---> 32 > 8
II. x < 0
If x is less than 0 but greater than -1, \(x^5\) will be greater than \(x^3\). Thus, (II) could be true.
E.g., if x = -0.5, \(x^5\) = -0.03125 and \(x^3\) = -0.125 ---> -0.03125 > -0.125
III. x < -1
If x is less than -1, \(x^5\) will always be less than \(x^3\). Thus, (III) cannot be true.
E.g., if x = -2, \(x^5\) = -32 and \(x^3\) = -8 ---> -32 < -8
Re: If x^5>x^3
[#permalink]
23 Aug 2024, 19:37
23 Aug 2024, 19:37
Could please someone explain to me why we are not considering x=1 here? for x>0
Which is not satisfying the condition here.
I think Only statement 3 could be true even x<0 includes x=-1 which doesn't satisfy the inequality.
Only x<-1 is possible??
Please correct me if I am wrong.
Thank you!!
Which is not satisfying the condition here.
I think Only statement 3 could be true even x<0 includes x=-1 which doesn't satisfy the inequality.
Only x<-1 is possible??
Please correct me if I am wrong.
Thank you!!
