SOLUTION: can you please help me with this equation? :] {{{ sqrt 2x-1 }}} + {{{ sqrt x+3 }}} = 0

Algebra ->  Radicals -> SOLUTION: can you please help me with this equation? :] {{{ sqrt 2x-1 }}} + {{{ sqrt x+3 }}} = 0      Log On


   

Question 223914: can you please help me with this equation? :]
+sqrt+2x-1+ + +sqrt+x%2B3+ = 0
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
This can be solved with some simple logic:
  • All square roots are non-negative (IOW they are either zero or positive).
  • Your equation says the sum of two square roots is 0
  • The only way two non-negative numbers can add up to zero is if both numbers are zero. (Think about this. After some thought I hope this is clear.)
  • There is no way for both of your suqare roots to be zero at the same time. (The only way the first square root can be zero is if x = 1/2. But if x = 1/2, then the second square root is not zero. And the only way for the second square root to be zero is if x = -3. But this does not make the first square root zero.)
  • So this equation is impossible. There are no solutions.

You could try some algebra to solve this. But at some point you would square both sides of the equation. And this would require that you check you answers. And checking your answers would show that none of them actually work!