Question 991173
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{{{sqrt(x+1)}}} + {{{sqrt(x-1)}}} = {{{sqrt(2x+1)}}}.


Square both sides:


{{{x + 1}}} + {{{2sqrt((x+1)*(x-1))}}} + {{{x-1}}} = {{{2x+1}}}.


Simplify:


{{{2x}}} + {{{2*sqrt(x^2-1))}}} = {{{2x+1}}},


{{{2*sqrt(x^2-1)}}} = {{{1}}}.


Square both sides again:


{{{4*(x^2-1)}}} = {{{1}}}. 


{{{4x^2}}} = {{{1 + 4}}} = {{{5}}},


{{{x^2}}} = {{{5/4}}},


x = +/- {{{sqrt(5)/2}}}.


Only positive root suits the original equation  (remember about the term  {{{sqrt(x-1)}}}).


<U>Answer</U>. &nbsp;x = {{{sqrt(5)/2}}}.