SOLUTION: If a^3b^5c^7 < 0 and b > 0, which of the following must be true?
I. ab < 0
II. ac < 0
III. a^2c^2 > 0
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Question 880568: If a^3b^5c^7 < 0 and b > 0, which of the following must be true?
I. ab < 0
II. ac < 0
III. a^2c^2 > 0
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Since , we know that , so .
That is good to know, in case we want to divide by those numbers.
For all and , and , because they are squares.
If , then .
So , and are positive, and so is their product, .
Then, starting with
,
we can divide both sides of the inequality by that positive product:
That simplifies to
NOTE:
Of course, also must be true if , which is a consequence of .
So for , is true if , and it is also true if ,
but III is not the answer they want,
and the answer that will help your grade is .
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