Question 65842
solve

square root of x - 15 + 1 = the square root of x
{{{sqrt(x-15)+1=sqrt(x)}}}
{{{sqrt(x-15)+1-1=sqrt(x)-1}}}
{{{sqrt(x-15)=sqrt(x)-1}}}
{{{(sqrt(x-15))^2=(sqrt(x)-1)^2}}}
{{{x-15=sqrt(x^2)-2sqrt(x)+1}}}
{{{x-15=x-2sqrt(x)+1}}}
{{{x-x-15-1=x-x-2sqrt(x)+1-1}}}
{{{-16=-2sqrt(x)}}}
{{{-16/-2=-2sqrt(x)/-2}}}
{{{8=sqrt(x)}}}
{{{(8)^2=(sqrt(x))^2}}}
{{{64=x}}}
check to make sure that this is not extraneous.
{{{sqrt(64-15)+1=sqrt(64)}}}
{{{sqrt(49)+1=8}}}
{{{7+1=8}}}
{{{8=8}}}
The solution {{{highlight(x=64)}}} is valid.
Happy Calculating!!!!