Question

Solve and check for extraneous solutions. " title=" \sqrt{3x+1} =x-1" alt=" \sqrt{3x+1} =x-1" align="absmiddle" class="latex-formula">

Answer 1

$D:3x+1\geq 0\wedge x-1\geq 0\\ D:3x\geq-1 \wedge x\geq1\\ D:x\geq-\frac{1}{3} \wedge x\geq1\\ D:x\geq1\\ \sqrt{3x+1}=x-1\\ 3x+1=(x-1)^2\\ 3x+1=x^2-2x+1\\ x^2-5x=0\\ x(x-5)=0\\ x=0 \vee x=5$

The solution is 5.
The extraneous solution is 0.