Question

Constructive proof: There exists an integer x such that: (x^3)/5 > x^2

Answer 1

`x>5`

Explanation:

We are asked to find an integer x such that
`(x^3)/(5)>x^2`.

First of all, we will multiply both sides of inequality by 5.

`(x^3)/(5)>x^2`

`(x^3)/(5)*5>5*x^2`

`x^3>5x^2`

Divide both sides by
`x^2`:

`(x^3)/(x^2)>(5x^2)/(x^2)`

`x>5`

Therefore, the value of x is any number greater than 5.