数列 a [ n ] において
a [ 1 ]= 3 , a [ 2 ] = 5 , a [ 3 ] = 7
( a [ n ] ) ( a [ n + 3 ] ) = ( a [ n + 2 ] ) ^ 2 - ( a [ n + 1 ] ) ^ 2
を満たすとき
| a [ n ] | < 14 / √ 3

a , b , c > 0 , a ^ 2 > b c
のとき
( a ^ 2 - b c ) ^ 2 ≧ k ( b ^ 2 - c a ) ( c ^ 2 - a b )
を満たす最大の k を求む