Prove the following inequality

  • Thread starter evagelos
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    Inequality
In summary, we are trying to prove the inequality \frac{a^4+b^4+c^4}{a^2b^2+a^2c^2+b^2c^2}\geq\frac{2u+3\lambda}{3(u+\lambda)} for all real numbers a,b,c (excluding zero) and natural numbers u,λ. The suggested approach is to use induction and subtract a constant from both sides of the inequality.
  • #1
evagelos
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Homework Statement



prove the following inequality:

Homework Equations



[tex]\frac{a^4+b^4+c^4}{a^2b^2+a^2c^2+b^2c^2}\geq\frac{2u+3\lambda}{3(u+\lambda)}[/tex]

for all the reals a,b,c different from zero and for all the natural u,λ

The Attempt at a Solution



induction i think in this case will make things worst
 
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  • #2
hi evagelos! :smile:

(try using the X2 tag just above the Reply box :wink:)

hint: subtract a constant from the lhs :wink:
 
  • #3


Sorry tiny-tim i don't get what you mean .What constant must i subtract from the l.h.s.
 
  • #4
that's for you to find out! :wink:
 
  • #5


you cannot subtract a constant, only, from the left hand side because then you change the inequality
 
  • #6
ok, then subtract it from both sides :smile:
 

What does it mean to "prove" an inequality?

Proving an inequality means to use logical reasoning and mathematical techniques to demonstrate that one side of the inequality is always greater or less than the other side.

Why is it important to prove inequalities?

Proving inequalities is important because it allows us to establish the validity of mathematical statements and to determine the relationship between different quantities.

What methods can be used to prove inequalities?

There are several methods that can be used to prove inequalities, including algebraic manipulation, induction, contradiction, and calculus techniques such as differentiation and integration.

Can inequalities be proven for all numbers or only certain numbers?

Inequalities can be proven for all numbers as long as the mathematical operations involved are well-defined and the numbers satisfy certain conditions, such as being real numbers.

What is the difference between a strict and non-strict inequality?

A strict inequality, denoted by <, >, or ≠, means that the two sides of the inequality are not equal and one side is strictly larger or smaller than the other. A non-strict inequality, denoted by ≤ or ≥, includes the possibility of the two sides being equal.

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