# How do you solve sqrt(x-17) = sqrt( x-1)?

Sep 23, 2015

You cannot solve it.

#### Explanation:

You cannot solve it since it is NOT an equality
(the part on the left is not equal to the part on the right)

Let's see what happens if I try to solve this, assuming the equality is correct . We have:
$\sqrt{x - 17} = \sqrt{x - 1}$
I would square both sides, since they are equal, it should give me the same:
$x - 17 = x - 1$
Now I can add 17 on both sides of the equality, since they are equal, the result should give me the same:
$x - 17 + 17 = x - 1 + 17$
$x - 0 = x + 16$
that is
$x = x + 16$

Now I can also subtract by x on both sides of the equality, since they are equal, the result should give me the same:
$x - x = x + 16 - x$
which is:
$0 = 16$
Wait a minute...
0 is not equal to 16!
This is impossible.
But so, what went wrong?
It turns out that our assumption was wrong.
We assumed the equality was correct.
And it wasn't.
So this equation was unsolvable right from the start.

Q.E.D.