Can You Prove This Inequality for Positive Real Numbers a,b,c,d with Sum of 1?

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In summary, "Proove number inequality" is a mathematical concept that involves using mathematical operations and logical reasoning to compare two numbers and prove which one is larger. It differs from regular inequalities in that it requires a formal proof. It can be used to compare any type of numbers, including whole numbers, fractions, decimals, and complex numbers. It can also be used for more than two numbers by combining inequality statements with logical operators. "Proove number inequality" is important because it allows for precise comparisons between numbers, which can be useful in various contexts.
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wnvl
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[tex]a,b,c,d\in\mathbb{R^{+}}\;\;,a+b+c+d=1.[/tex]

Then prove that

[tex]\left( a+\dfrac{1}{b}\right).\left(b+\dfrac{1}{c}\right).\left(c+\dfrac{1}{a}\right)\geq \left(\dfrac{10}{3}\right)^3[/tex]

Anyone an idea on how to start with this exercise?
 
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  • #2
wnvl said:
[tex]a,b,c,d\in\mathbb{R^{+}}\;\;,a+b+c+d=1.[/tex]

implies 0<a+b+c<1
 

1. What is "Proove number inequality"?

"Proove number inequality" is a mathematical concept used to compare two numbers and determine which one is larger. It involves using a series of mathematical operations and logical reasoning to prove the inequality statement.

2. How is "Proove number inequality" different from regular inequalities?

"Proove number inequality" is different from regular inequalities in that it requires a formal proof to demonstrate the truth of the inequality statement. This involves using mathematical operations and logical reasoning, rather than just comparing two numbers.

3. What types of numbers can be compared using "Proove number inequality"?

"Proove number inequality" can be used to compare any type of numbers, including whole numbers, fractions, decimals, and even complex numbers. The process for proving the inequality statement may differ slightly depending on the type of numbers being compared.

4. Can "Proove number inequality" be used for more than two numbers?

Yes, "Proove number inequality" can be used for more than two numbers. You can compare multiple numbers by using a series of inequality statements and combining them with logical operators, such as "and" or "or".

5. Why is "Proove number inequality" important?

"Proove number inequality" is important because it allows us to make precise comparisons between numbers and determine which one is larger. This can be especially useful in mathematical and scientific contexts, as well as in everyday life situations where we need to make decisions based on numerical values.

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