Question

Solve and check for extraneous solutions.

`√(3x+1) =x-1`

Answer 1

`D:3x+1\geq 0\wedge x-1\geq 0\\ D:3x\geq-1 \wedge x\geq1\\ D:x\geq-(1)/(3) \wedge x\geq1\\ D:x\geq1\\ √(3x+1)=x-1\\ 3x+1=(x-1)^2\\ 3x+1=x^2-2x+1\\ x^2-5x=0\\ x(x-5)=0\\ x=0 \vee x=5`

The solution is 5.
The extraneous solution is 0.