The conjecture can be written mathematically as x^2>x.
See solution.
Practice makes perfect
Let's begin by writing the given conjecture as an inequality.
The value of x^2 is always greater than
The value of x
⇓
x^2 > x
Note that x^2 means that we multiply x by itself. This expression will always be greater than x for the intervals x<- 1 and x>1. This means for values that fall in the interval - 1≤ x≤ 1, the inequality is not true. Below we see two examples.
ccc
1^2? > 1 &⇒ & 1 ≯ 1
0.5^2? > 0.5 &⇒ & 0.25 ≯ 0.5
Therefore, we have found a counterexample proving the conjecture false.
