Question 33877
<pre>
sqrt(2x-5)-sqrt(x-3)=1
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Whatever the other person who responded did, doesn't make sense, at all, to this author. Yet,
it's quite surprising that he/she got one of the solutions. But, there's another one!

  {{{sqrt(2x - 5) - sqrt(x - 3) = 1}}}, with {{{x >= 3}}}  
          {{{sqrt(2x - 5) = 1 + sqrt(x - 3)}}} ----- Adding {{{sqrt(x - 3)}}} to both sides
       {{{(sqrt(2x - 5))^2 = 1^2 + 2sqrt(x - 3) + (sqrt(x - 3))^2}}}
            {{{2x - 5 = 1 + 2sqrt(x - 3) + x - 3}}}
            {{{2x - 5 = 2sqrt(x - 3) + x - 2}}}
      {{{2x - 5 - x + 2 = 2sqrt(x - 3)}}}
             {{{x - 3 = 2sqrt(x - 3)}}}
           {{{(x - 3)^2 = (2sqrt(x - 3))^2}}} ---- Squaring each side
        {{{x^2 - 6x + 9 = 4(x - 3)}}}
        {{{x^2 - 6x + 9 = 4x - 12}}}
{{{x^2 - 6x + 9 - 4x + 12 = 0}}}
     {{{x^2 - 10x + 21 = 0}}}
  (x - 7)(x - 3) = 0
   x - 7 = 0     OR    x - 3 = 0
      <font color = red><font size  = 4><b>x = 7    OR      x = 3</font></font></b>

As 7 > 3 and 3 = 3, the above constraint, {{{x >= 3}}} is satisfied. Therefore, both solutions are ACCEPTABLE!!</pre>