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# Homogeneous Inequality

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

Note by Neel Khare
5 months, 2 weeks ago

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A 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. · 5 months, 1 week ago

I didn't understand the first example Degree 4 ?? · 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. :) · 5 months, 1 week ago