blackbird02
  • blackbird02
Help in proving this inequality using the concepts or theorems on the properties of real numbers
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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blackbird02
  • blackbird02
blackbird02
  • blackbird02
Prove that if a>0, b<0, then \[ab+\frac{ b }{ a }<0\]
triciaal
  • triciaal
|dw:1442641989956:dw|

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blackbird02
  • blackbird02
what does ve stand for?
triciaal
  • triciaal
sorry, -ve = negative and +ve = positive
blackbird02
  • blackbird02
I'm sorry, but I still don't get it. What would be my starting equation in the proving?
zzr0ck3r
  • zzr0ck3r
\(ab<0 \text{ and } \frac{a}{b}<0\) so \(ab+\frac{a}{b}<0\)
blackbird02
  • blackbird02
@zzr0ck3r How would I prove this using the concepts or theorems on the properties of real numbers?
blackbird02
  • blackbird02
@Hero any idea how to prove this?
Hero
  • Hero
Are you still here.
blackbird02
  • blackbird02
Yeah
Hero
  • Hero
blackbird02
  • blackbird02
@Hero just a clarification, in the seventh row, what is the equation? is it ab<0 +b/a<0 Or b/a<0 should be on another line?
Hero
  • Hero
It's one line: Two inequalities being added together
blackbird02
  • blackbird02
Oh, okay. I get it now. Thank you so much!
Hero
  • Hero
It's written exactly as it Should be
triciaal
  • triciaal
@hero can you explain the step where you have "flip sign"?
Hero
  • Hero
b is negative If you multiply both sides of a>0 by a negative number, you have to invert the inequality symbol
blackbird02
  • blackbird02
@Hero Thank you so much!
triciaal
  • triciaal
sorry, well thanks but that's the only place we differ on why a negative times a positive is negative. multiplication is group addition and we have a constant times a negative entity so it is more negative.
zzr0ck3r
  • zzr0ck3r
"multiplication is group addition" ?
triciaal
  • triciaal
@zzr0ck3r yes example 3 * 2 = 2 + 2 + 2 etc
triciaal
  • triciaal
maybe repeated addition is better
zzr0ck3r
  • zzr0ck3r
addition is the operation on the reals as a group multiplication is the other operation on the reals as a ring
zzr0ck3r
  • zzr0ck3r
how would you write out (1/2)*(1/3) in those terms?
triciaal
  • triciaal
what?
zzr0ck3r
  • zzr0ck3r
google groups and rings.
zzr0ck3r
  • zzr0ck3r
we start with a group an one operation addition we extend this idea to another operation called multiplication, once we have two operations and a few more properties we have a ring. we then include multiplicative inverses to close it up, and we get a field. All I am saying, is that sentence made no sense. ...

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