The same squared equation, different answers

8 written marks

Consider the equation \(\sqrt{x+1}=x-1\).

1. State the restrictions on \(x\) imposed by the square root and by the sign of the right-hand side. Combine them.

   [2]

2. Solve the equation exactly.

   [3]

3. Now solve \(\sqrt{x+1}=1-x\). Explain why the answer is different although squaring gives the same quadratic.

   [3]

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