loriebarlam
loriebarlam loriebarlam
  • 16-01-2020
  • Mathematics
contestada

Prove that the inequality (a+1)·(a+1)>(a−1)·(a−1) is not true for some values of a.

Respuesta :

sqdancefan
sqdancefan sqdancefan
  • 27-01-2020

Explanation:

Consider the case a = -1. Then the expression becomes ...

  (-1+1)(-1+1) > (-1-1)(-1-1) . . . . test case

  0·0 > (-2)(-2) . . . . . simplified a bit

  0 > 4 . . . . . . . . NOT TRUE

_____

If we subtract the right side from both sides, the inequality becomes ...

  (a+1)(a+1) -(a-1)(a-1) > 0

  a² +2a +1 -(a² -2a +1) > 0

  4a > 0

  a > 0

The inequality is only true for positive values of "a". For a ≤ 0, the inequality will not be true.

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