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.

#Algebra

Easy Math Editor

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`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
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Comments

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

Vicky Ricky - 3 years, 5 months ago

how i solve the problem

shamindra das - 3 years, 5 months ago

I can't understand how to do it

Soma Chattoraj - 3 years, 5 months ago

Show solution please

Naaz Hussain - 3 years, 5 months ago

i have written the solution.

Vicky Ricky - 3 years, 5 months ago

Please show the solution.

Soma Chattoraj - 3 years, 5 months ago

i have written the solution

Vicky Ricky - 3 years, 5 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}`	$\boxed{123}$