Cambridge exercise 3A q)12 --------> Inequalities (1 Viewer)

[SammyT123]

12.

If a>b and b is not equal to zero, prove:

a) -a<-b
b) ab^2 > b^3

I understand these questions (common sense ) but how exactly would I do an official proof for them?

Thanks
-SammyT

 

[InteGrand]

12.

If a>b and b is not equal to zero, prove:

a) -a<-b
b) ab^2 > b^3



I understand these questions (common sense ) but how exactly would I do an official proof for them?

Thanks
-SammyT

Given:

a) Add to both sides of the above, and the desired inequality is reached.
b) (you can multiply an inequality through by a positive number, which is)

 

[SammyT123]

Given:

a) Add to both sides of the above, and the desired inequality is reached.
b) (you can multiply an inequality through by a positive number, which is)

That's all?
That was my answer but it didn't seem right that a question would be this simple


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[braintic]

That's all?
That was my answer but it didn't seem right that a question would be this simple


Sent from my iPhone using Tapatalk

Alternatively:
ab² - b³ = b²(a-b)
> 0 since a>b & b²>0

ab² > b³

 

[SammyT123]

Alternatively:
ab² - b³ = b²(a-b)
> 0 since a>b & b²>0

ab² > b³

Thanks


Sent from my iPhone using Tapatalk