SOLUTION: Find all real number solutions of the equation algebraically. {{{ sqrt(2x+1) }}} - {{{ sqrt(x+1) }}} = 2 I found that x = 0 and x = 8 but both solutions are extraneous and

Algebra ->  Radicals -> SOLUTION: Find all real number solutions of the equation algebraically. {{{ sqrt(2x+1) }}} - {{{ sqrt(x+1) }}} = 2 I found that x = 0 and x = 8 but both solutions are extraneous and       Log On


   

Question 188628: Find all real number solutions of the equation algebraically.
+sqrt%282x%2B1%29+ - +sqrt%28x%2B1%29+ = 2

I found that x = 0 and x = 8 but both solutions are extraneous and therefore I think the equation has no solution. Is this correct?
Answer by solver91311(24713) About Me  (Show Source):
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Square both sides:



Simplify:





Square both sides:













Root is extraneous





Answer checks.

This problem brings to mind a very interesting brain teaser. The number 48 is very special. If you add 1, you get 49 which is a perfect square. If you divide it by 2 and then add 1, you get another perfect square (48/2 = 24, 24 + 1 = 25). Find three other integers with the same property.

John