Question

Solve the equation: √x+1 = x-1

Answer 1

√x + 1 = x - 1
↓
√x = x - 1 + 1
↓
√x = x

Since 1 is the only real number whose square root equals itself, we can safely assume that x = 1.
Hope that helped! =)

Answer 2

`√(x+1) = x - 1 \\ \\ x + 1 = (x - 1)^2 \\ \\ x + 1 = x^2 - 2x + 1 \\ \\ x = x^2 - 2x \\ \\ x - x^2 + 2x = 0 \\ \\ 3x - x^2 = 0 \\ \\ x(3 - x)= 0 \\ \\ x = 0,3 \\ \\ x = 0 \ is \ false \\ \\ x = 3`

The final result is, x = 3.

The solutions we gather were x = 0,3.
We dropped x = 0 from the equation since it does not become true, so we are left with x = 3.