Are you so sure?

Algebra Level 4

For $x\in\mathbb{Z}$ , $10<x^{2}<100$ Find $x_{\text{min}}-x_{\text{max}}$ .

2 solutions

A Former Brilliant Member
Apr 3, 2015

As $x$ is a integer the maximum value of $x$ is 9.

Now, this is the tricky part. $(x)^{2} =(-x)^{2}$ which means that -9 will be least value of $x$

Therefore answer =-9-9 = -18

Is this question worth of 4th level?

Vraj Mistry - 6 years ago

Nice solution!Entered $-8$ in first try then saw that $-9^{2}$ and got right in second try!

Harsh Shrivastava - 6 years, 2 months ago

Vaibhav Prasad
Apr 3, 2015

The largest square under hundred is $81$ , which is $9^2$ . Thus

$x_{max}=9$

But $x$ can even be a negative integer as the square of a negative integer is a positive. Thus

$x_{min}=-9$

Hence $x_{min}-x_{max}=-9-9=-18$