Solve and Check√x-6=√3-√x
Assuming you meant
√(x-6)=√3-√x, we square both sides and get
x-6 = 3-2√(3x)+x
-9 = -2√(3x)
9/2 = √(3x)
81/4 = 3x
x = 27/4
Check: √(3/4) = √3-√(27/4)
√3/2 = √3(1-3/2)
√3/2 = -√3/2
Nope.
If you meant
√x - 6 = √3-√x we have
2√x = 6+√3
4x = 36+12√3+3
4x = 39+12√3
x = 39/4 + 3√3
I'll let you verify the solution.