×

# Tessellate S.T.E.M.S - Mathematics - School - Set 2 - Subjective Problem

For positive real numbers $$a,b,c,d,e$$ prove that $(a^3-a+2)(b^3-b+2)(c^3-c+2)(d^3-d+2)(e^3-e+2) \geq \left( S_4- S_2 +1 \right)^2$

where $$S_4 = abcd + abce + abde + acde + bcde \\ S_2 = ab+ac+ad+ae+bc+bd+be+cd+ce+de$$.

This problem is a part of Tessellate S.T.E.M.S.

2 weeks, 1 day ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. 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 1paragraph 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} $$\boxed{123}$$

Sort by:

- 4 days, 3 hours ago

i have written the solution.

- 4 days, 1 hour ago

I can't understand how to do it

- 4 days, 4 hours ago

just break the brackets by simple multiplying and then use AM>=GM and then it will be done.

- 1 week, 1 day ago

how i solve the problem

- 3 days, 20 hours ago

- 4 days, 4 hours ago

i have written the solution

- 4 days, 1 hour ago