How Would You Solve This?
I have many other problems similar to this one:
1.√3-x =2-√x+1
If you mean
√(3-x) = 2-√(x+1)
just square both sides:
3-x = 4 - 4√(x+1) + (x+1)
2x+2 = 4√(x+1)
now factor out a 2 and square again:
x^2 + 2x + 1 = 4(x+1)
x^2 - 2x - 3 = 0
(x-3)(x+1) = 0
x = -1 or 3
However, we have squared things twice, so there's a good chance that we have some extraneous roots. Check them:
√(3-(-1)) =? 2-√(-1+1) yes
√(3-3) =? 2-√(3+1) yes