Question

5. Find a counterexample to show that the following con-
jecture is false.
Conjecture: For all numbers x, x4 > x.

Help please

Answer 1

Answer:  see below

Step-by-step explanation:

Any value x such that |x| < 1 will make the conjecture false

In simpler words, let x be a fraction between 0 and 1.

One example: Let x = $\dfrac{1}{2}$

Then x⁴ = $\bigg(\dfrac{1}{2}\bigg)^4$

             = $\dfrac{1}{16}$

$\dfrac{1}{16}$ < $\dfrac{1}{2}$

so the conjecture is false.