# Another Inequality #2

Algebra Level 5

$\large{(a^2 - bc)^2 > k(b^2 - ca)(c^2 - ab)}$

Find the greatest real number $$k$$ such that for any positive $$a,b,c$$ with $$a^2 > bc$$, the above inequality satisfies. Submit the value of $$k$$ upto three correct places of decimals.

×