Solution assignment 04 Root equations

Solve:

$\sqrt{x+2}-\sqrt{x-1}=-1$

The following conditions have to be met:

$x\geq{-2}$ and $x\geq1$

so:

$x\geq1$

We cannot remove all root functions at once by squaring. One time squaring yields:

$(x+2)+(x-1)-2\sqrt{(x+2)(x-1)}=1$

$2x+1-2\sqrt{(x+2)(x-1)}=1$

$\sqrt{(x+2)(x-1)}=x$

Now we can square again:

$(x+2)(x-1)=x^2$

$x=2$

This solution does not satisfy the original equation which thus has no solution.