Disuguaglianze importanti in matematica

Disuguaglianze importanti in matematica Di Cristiano Armellini cristiano.armellini@alice.it

Disuguaglianza 1(a − b) = a + b − 2ab > 0 2 2 2n = ab a +b 2 2n< 2

Disuguaglianza 2(a − b) = a − b − 3a b + 3ab > 0 3 3 3 2 2a>bd = a −bn = ab a −b 3 3d< 3n

Disuguaglianza 3x − sx + n = 0 2n = ab s = a+bdelta = s − 4n > 0 2 2 sn< 4

Disuguaglianza 4a 2 − b 2 = (a − b)(a + b) > 0s = a+bd = a −b > 0sd = a − b > 0 2 2s>2 n a2 − b2d< 2 n

Disuguaglianza 5(a − b) 4 = a 4 + b 4 + 6a 2b 2 − 4ab(a + b) > 0n = ab6n − 4ns + a + b > 0 2 4 4s = a+b a 4 + b 4 + 6n 2s< 4n

Disuguaglianza 6x, y > 0, s = x + y, n = xyx + y = ( x + y ) − 3xy ( x + y ) > 0 3 3 3( x + y ) 2 − 3 xy > 0s 2 > 3n, s > 3n

Disuguaglianza 7x + y = ( x + y ) − 2 xy > 0 2 2 2s = x+ yn = xys − 2n > 0 2s > 2n

by Cristiano Armellini