Break down and solve the equation √x+3=√x+13?

Question

Break down and solve the equation √x+3=√x+13? I have tried to look for solutions and everywhere I look it said that there isn't one but my question says different.

Answer 1

If the equation is √(x+13) = √x+3, then:

 

Square both sides to obtain x+13 = x + 6√x + 9

 

Isolating the remaining radical term, we have 6√x = 4

 

So, √x = 2/3

 

        x = 4/9  

 

 

Answer 2

You equation is ambiguous as written.  It's not clear what is under either radical.  If it's

 

     √(x+3) = √(x+13)

 

Then there is no solution.  Square both sides:

 

     x + 3 = x + 13

 

Subtract x from both sides:

 

     3 = 13

 

No solution!  However, if it's:

 

     √(x) + 3 = √(x+13)

 

Then square both sides:

 

     x + 6√x + 9 = x + 13

     6√x = 4

     √x = 2/3

     x = 4/9