Waste less time on Facebook — follow Brilliant.
×

Is this proof valid? (1)

I have a book, which states this inequality and need to be proof. Absolutely, this is a problem.

Given \(a,b \in \mathbb{R}^+\) and \(a\neq b\), proof that \[a^{3} +b^{3} > a^{2}b +ab^{2}\]

Proof: since \(a \neq b\), obviously that \[a+b>0\] \[(a-b)^2>0\]

Multiply both ineqs and we have \[(a+b)(a-b)^2>0\] \[(a+b)(a^2-2ab+b^2)>0\] \[a^3-a^2b-ab^2+b^3>0\] \[a^3+b^3>a^2b + ab^2\]

Done!

Is that valid? Comments will be appreciated!

Note by Figel Ilham
2 years, 7 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears 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} \( \boxed{123} \)

Comments

There are no comments in this discussion.

×

Problem Loading...

Note Loading...

Set Loading...