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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<    ...
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  ...
Disuguaglianza 6x, y > 0, s = x + y, n = xyx + y = ( x + y ) − 3xy ( x + y ) > 0 3     3            3( x + y ) 2 − 3 xy > ...
Disuguaglianza 7x + y = ( x + y ) − 2 xy > 0 2    2         2s = x+ yn = xys − 2n > 0 2s > 2n
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Disuguaglianze importanti in matematica

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Disuguaglianze importanti in matematica

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Disuguaglianze importanti in matematica

  1. 1. Disuguaglianze importanti in matematica Di Cristiano Armellini cristiano.armellini@alice.it
  2. 2. Disuguaglianza 1(a − b) = a + b − 2ab > 0 2 2 2n = ab a +b 2 2n< 2
  3. 3. Disuguaglianza 2(a − b) = a − b − 3a b + 3ab > 0 3 3 3 2 2a>bd = a −bn = ab a −b 3 3d< 3n
  4. 4. Disuguaglianza 3x − sx + n = 0 2n = ab s = a+bdelta = s − 4n > 0 2 2 sn< 4
  5. 5. 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
  6. 6. 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
  7. 7. 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
  8. 8. Disuguaglianza 7x + y = ( x + y ) − 2 xy > 0 2 2 2s = x+ yn = xys − 2n > 0 2s > 2n

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