Question 709801
{{{ sqrt(x) - sqrt(x-45) = 3 }}}.....square both sides


{{{ (sqrt(x) - sqrt(x-45))^2 = 3^2 }}}


{{{ (sqrt(x))^2 - 2sqrt(x)*sqrt(x-45)+(sqrt(x-45))^2 = 9 }}}


{{{ x - 2sqrt(x)*sqrt(x-45)+(x-45) = 9 }}}


{{{ x - 2sqrt(x(x-45))+x-45 = 9 }}}


{{{ 2x - 2sqrt(x(x-45)) = 9+45 }}}


{{{  - 2sqrt(x(x-45)) =-2x+54 }}}


{{{  sqrt(x(x-45)) =-2x/-2+54/-2 }}}


{{{  sqrt(x(x-45)) =x-27 }}}


{{{  (sqrt(x(x-45)))^2 =(x-27)^2 }}}...........square both sides


{{{  x(x-45) =x^2-54x+729 }}}


{{{  x^2-45x =x^2-54x+729 }}}


{{{  cross(x^2)-45x =cross(x^2)-54x+729 }}}


{{{  -45x =-54x+729 }}}


{{{  -45x+54x =729 }}}


{{{ 9x =729 }}}


{{{ x =729/8 }}}


{{{ highlight(x =81) }}}


check:

{{{ sqrt(x) - sqrt(x-45) = 3 }}}....plug in {{{ highlight(x =81) }}}


{{{ sqrt(81) - sqrt(81-45) = 3 }}}

{{{ 9 - sqrt(36) = 3 }}}

{{{ 9 - 6 = 3 }}}

{{{ 3 = 3 }}}