can anyone help me with this proof.

Question

praxer · Answer

$$a^2+b^2+c^2-(2ab+2bc+2ca)\ge \frac{ 4 }{ \sqrt{F} }$$

praxer · Answer

where a,b,c are the sides of a triangle and F is the area.

praxer · Answer

Someone please give a hint,

debbieg · Answer

I'm wondering if it has something to do with Heron's formula? http://www.mathsisfun.com/geometry/herons-formula.html Sorry, I'd try to work with you on it, but I'm short on time right now.

debbieg · Answer

Maybe @amistre64 has an idea....?

amistre64 · Answer

proof, by induction?

praxer · Answer

induction ?

amistre64 · Answer

you cant possibly test each and every triangle can you?

amistre64 · Answer

the left side is almost:  (a-b-c)^2

praxer · Answer

I am not getting anything could you please help me more in this matter.

amistre64 · Answer

$$a^2+b^2+c^2-(2ab+2bc+2ca)\ge \frac{ 4 }{ \sqrt{F} }$$
$$(a-b-c)^2-4bc\ge \frac{ 4 }{ \sqrt{F} }$$

praxer · Answer

I have to prove the equation it is not provided, i have to prove with the help of the given information,

praxer · Answer

May be I require a diagram and then proceed with prerequisite.

amistre64 · Answer

diagrams are always nice when they can be drawn

amistre64 · Answer

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