Question 260105
{{{sqrt(x-1)=-2}}} Start with the given equation.



{{{x-1=4}}} Square both sides.


 
{{{x=4+1}}} Add 1 to both sides.



{{{x=5}}} Combine like terms.



So the possible solution is {{{x=5}}}, but we need to check it.



{{{sqrt(x-1)=-2}}} Start with the given equation.



{{{sqrt(5-1)=-2}}} Plug in {{{x=5}}}



{{{sqrt(4)=-2}}} Subtract



{{{2=-2}}} Take the square root of 4 to get 2.



Since the equation is NOT true, this means that there are no solutions. Another way of saying that there are no solutions is to say that the solution set of the given equation is the empty set *[Tex \LARGE \empty] (the symbol *[Tex \LARGE \empty] stands for the empty set). I think this is what your book is telling you.