Question

Find a counterexample to show that the conjecture is false. The value of x² is always greater than the value of x. a. x = 0

b. x = 1
c. x = 2 d. x = -1

Answer 1

To disprove the conjecture, we find counterexamples where x² is not greater than x.

Step-by-step explanation:

The conjecture states that the value of x² is always greater than the value of x. To find a counterexample that proves this conjecture false, we need to find a value of x for which x² is not greater than x. Let's evaluate the given options:

a. For x = 0, we have 0² = 0 which is not greater than 0. This is a counterexample.

b. For x = 1, we have 1² = 1 which is not greater than 1. This is a counterexample.

c. For x = 2, we have 2² = 4 which is greater than 2. This does not disprove the conjecture.

d. For x = -1, we have (-1)² = 1 which is not greater than -1. This is a counterexample.

So, the counterexamples to the conjecture are x = 0, x = 1, and x = -1.