Prove the following inequality

[evagelos]

Homework Statement

prove the following inequality:

Homework Equations

$$\frac{a^4+b^4+c^4}{a^2b^2+a^2c^2+b^2c^2}\geq\frac{2u+3\lambda}{3(u+\lambda)}$$

for all 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

 

[tiny-tim]

hi evagelos!

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

hint: subtract a constant from the lhs

 

[evagelos]

Sorry tiny-tim i don't get what you mean .What constant must i subtract from the l.h.s.

 

[tiny-tim]

that's for you to find out!

 

[evagelos]

you cannot subtract a constant, only, from the left hand side because then you change the inequality

 

[tiny-tim]

ok, then subtract it from both sides