if
a,b,c are R*
and if
a^3/bc+b^3/ac+c^3/ab > a+b+c
prove that
abc > 0
Is there something wrong with this problem? Because the LHS can be manipulated as,Originally Posted by oneplan4u
$\displaystyle \frac{a^4+b^4+c^4}{abc}>a+b+c$
But if $\displaystyle a=b=c=x$ then we have,
$\displaystyle \frac{3x^4}{x^3}>3x$
Thus,
$\displaystyle 3x>3x$
Which is not true, perhaps you mean $\displaystyle \geq$.