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
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Question 188628: Find all real number solutions of the equation algebraically.
- = 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) (Show Source): You can put this solution on YOUR website!
Square both sides:
 - 2 sqrt{(2x+1)(x+1)} + (x + 1) = 4)
Simplify:
(x+1)} = -3x + 2)
(x+1)} = \frac{3x}{2} - 1)
Square both sides:
(x+1) = \frac{9x^2}{4} - 3x + 1)
 = 0)
+1}-sqrt{(0)+1} = 1 - 1 = 0 \neq 2)
Root is extraneous
+1}-sqrt{(24)+1} = sqrt{49} - sqrt{25} = 7 - 5 = 2)
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
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