Question

What is the solution set for x in the equation below?

Answer 1

(-1, 0)

Step-by-step explanation:

Given the radical expression;

`\sqrt[]{x+1}-1=x`

Add 1 to both sides;

`\begin{gathered} \sqrt[]{x+1}-1+1=x+1 \\ \sqrt[]{x+1}=x+1 \end{gathered}`

Square both sides

`\begin{gathered} (\sqrt[]{x+1})^2=(x+1)^2 \\ x+1=(x+1)^2 \\ 1=x+1 \\ Swap \\ x+1=0 \\ x=0-1 \\ x=-1 \end{gathered}`

Hence the solution to the radical expression is (-1, 0)