Question 965230
{{{ sqrt(x) - sqrt( x-2 ) - 1 = 0 }}}
{{{ sqrt(x) = sqrt( x-2 ) + 1 }}}
Square both sides
{{{ x = ( sqrt( x-2 ) + 1 )^2 }}}
{{{ x = x-2 + 2*sqrt( x-2 ) + 1 }}}
subtract {{{ x }}} from both sides
{{{ 0 = -2 + 2*sqrt( x-2 ) + 1 }}}
{{{ 2*sqrt( x-2 ) = 1 }}}
{{{ sqrt( x-2 ) = 1/2 }}}
Square both sides
{{{ x - 2 = 1/4 }}}
{{{ x = 8/4 + 1/4 }}}
{{{ x = 9/4 }}}
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check:
{{{ sqrt(x) - sqrt( x-2 ) - 1 = 0 }}}
{{{ sqrt( 9/4 ) - sqrt( 9/4 - 2 ) - 1 = 0 }}}
{{{ 3/2 - sqrt( 9/4 - 8/4 ) - 1 = 0 }}}
{{{ 3/2 - sqrt( 1/4 ) - 1 = 0 }}}
{{{ 3/2 - 1/2 - 2/2 = 0 }}}
{{{ 3/2 - 3/2 = 0 }}}
{{{ 0 = 0 }}}
OK