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

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

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.

Sharky Kesa - 4 years, 3 months ago

I didn't understand the first example Degree 4 ??

A Former Brilliant Member - 4 years, 3 months 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. :)

Sharky Kesa - 4 years, 3 months ago

@Sharky Kesa – Thanks Yes I need to revise degrees of multi variable polynomial Thanks for telling me

A Former Brilliant Member - 4 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$