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Dima020 [189]
3 years ago
12

Samantha conjectures that for x < -1, it is true that x5 - 2 > x. Is her conjecture correct? Why or why not?

Mathematics
1 answer:
Ronch [10]3 years ago
4 0

Answer:

  The conjecture cannot work for any negative numbers, It works for x > 1.3.

Step-by-step explanation:

An odd power preserves the sign. For |x| > 1, the power increases the magnitude. For x < 0, adding -2 only increases the magnitude more. A negative number of larger magnitude will not be "greater than" the reference. It will be "less than."

It only takes a counterexample to show the conjecture is incorrect.

  x^5 -2 ?? x

  (-2)^5 -2 ?? (-2)

  -32 -2 ?? -2

  -34 < -2 . . . . . . not greater than

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