Question 29608
{{{ sqrt(2x+5) = 2 + sqrt(x-2) }}}


Now square both sides:
{{{ (sqrt(2x+5))^2 = (2 + sqrt(x-2))^2 }}}
{{{ (2x+5) = (2 + sqrt(x-2))(2 + sqrt(x-2)) }}}
{{{ (2x+5) = (2(2) + 2sqrt(x-2) + 2sqrt(x-2) + sqrt(x-2)sqrt(x-2)) }}}
{{{ 2x+5 = (4 + 4sqrt(x-2) + (x-2)) }}}
{{{ 2x+5 = (4 + 4sqrt(x-2) + x-2) }}}
{{{ x+3 = 4sqrt(x-2) }}}


Square both sides again:
{{{ (x+3)^2 = (4sqrt(x-2))^2 }}}
{{{ x^2+6x+9 = 16(x-2) }}}
{{{ x^2+6x+9 = 16x-32 }}}
{{{ x^2-10x+41 = 0 }}}


Put this into the quadratic formula and you get {{{5 +- 4i }}} as the answer - if you have done the topic "Complex numbers". If not, then your answer is "there is no answer" :-)


jon.