Chapter 10 - Radical Expressions and Equations - 10-4 Solving Radical Equations - Practice and Problem-Solving Exercises - Page 624: 26

$n=-4$ is extraneous

$Given,$ $\sqrt (12-n)=n$ Checking for $n=-4$ : $L.H.S=\sqrt (12-(-4))=\sqrt 16=4$ $R.H.S=-4$ $L.H.S$ does not equal $R.H.S$,hence $n=-4$ is extraneous Checking for $n=3$: $L.H.S=\sqrt (12-3)=\sqrt 9=3$ $R.H.S=3$ $L.H.S=R.H.S$,hence $n=3$ is not extraneous