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

##### 1 Answer

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:

I would square both sides, since they are equal, it should give me the same:

Now I can add 17 on both sides of the equality, since they are equal, the result should give me the same:

Now I do the addition/subtraction:

that is

Now I can also subtract by x on both sides of the equality, since they are equal, the result should give me the same:

which is:

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.