SOLUTION: (x)^1/2-(x+3)^1/2=0
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Question 181801: (x)^1/2-(x+3)^1/2=0
Found 2 solutions by checkley77, solver91311:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
(x)^1/2-(x+3)^1/2=0
(x)^1/2=(x+3)^1/2
sqrtx=sqrt(x+3)
x=x+3
x-x=3
0=3 no unique solution for x.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
^{\frac{1}{2}} = 0)
If you first add ^{\frac{1}{2}} )
to both sides of the equation and re-write the fractional exponents as radicals:
You can readily see that this equation has no solution. That's because over the most restrictive domain (the left hand side function), namely
,
The values of the two sides of the equation will differ by a factor of 
at the low end of the domain and will differ by a decreasing amount as x gets larger, but the difference can never be exactly zero.
This is the reason that using ordinary solution methods on this equation results in an absurdity:
Square both sides:
Add -x to both sides:
Absurd.
Therefore, the solution set of the given equation is the empty set.
John
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