Answer:
This problem of equations involving surds can be solved by :
Firstly,square both sides of the equation to do away with the surd
(√x+3)²=(x-3)²
Next,we do away with the surd or let me put it as sign of square root and FOIL out the RHS
x+3=x²-6x+9
Rearranging leads to:
x²-6x-x+9-3=0
x²-7x+6=0 which factorises to:
(x-6)(x-1)=0
Finding the zeros leads to
x=6 or 1
We now conduct a test to see which value(s) of x satisfy the equation
√6+3=6-3
√9=3
3=3, so x=6 is true
Now for 1,
√1+3=1-3
√4 is not equal to -2
Therefore we conclude that x=6