I have read may texts saying that if it's a homogeneous inequality Then you can assume abc =1 or a+b+c =1 But what is a homogeneous inequality Can anybody explain

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewestA homogeneous inequality is an inequality in which all terms have the same degree. For example, \(abc^2 + a^4 + ab^3 \geq 13bc^3\) is a homogeneous inequality, since all the terms have degree 4, whereas \(a^3+ab+b^4 \geq 12\) is a heterogeneous inequality since all the terms don't have the same degree. – Sharky Kesa · 5 months, 1 week ago

Log in to reply

– Neel Khare · 5 months, 1 week ago

I didn't understand the first example Degree 4 ??Log in to reply

– Sharky Kesa · 5 months, 1 week ago

The term \(abc^2\) has degree 4, doesn't it? The term \(a^4\) also has degree 4. The term \(bc^3\) has degree 4, and finally, \(bc^3\) has degree 4. Therefore, the overall expression has degree 4. Recap on your polynomial definitions (including degrees of multivariate polynomials) to understand. :)Log in to reply

– Neel Khare · 5 months, 1 week ago

Thanks Yes I need to revise degrees of multi variable polynomial Thanks for telling meLog in to reply