There are several ways to prove a mathematical statement. These ways include: by contradiction, by induction, contraposition, etc
To prove the statement, we make use of proof by contradiction
From the question:
x is a composite number such that: x > 1
This means that 1 < a < x is a factor of x
This can be represented as:
[tex]x = a * b[/tex]
Where:
Assume that b is less than or equal to a.
Also, let
[tex]b > \sqrt x[/tex]
This means that:
[tex]\sqrt x < b \ge a[/tex]
The above becomes
[tex]\sqrt x < a[/tex]
Rewrite as:
[tex]a > \sqrt x[/tex]
So, we have:
[tex]x = a * b > \sqrt x * \sqrt x = x[/tex]
The above means that:
[tex]x > x[/tex]
The above inequality is a contradiction because, a number x cannot be greater than itself
This means that, the supposition is wrong.
Hence, the given statement has been proved by contradiction
Read more about proof by contradiction at:
https://brainly.com/question/8062770
