Chapter 10 - Radical Expressions and Equations - 10-4 Solving Radical Equations - Practice and Problem-Solving Exercises - Page 623: 24

$m=2.5$

$Given,$ $\sqrt (3m+1)=\sqrt (7m-9)$ Squaring,we get: $3m+1=7m-9$ $3m+1+9=7m-9+9$ $3m+10-3m=7m-3m$ $4m=10$ $m=10\div4=2.5$ We need to check by putting the obtained value in the original equation : $L.H.S=\sqrt(3X2.5+1) =\sqrt 8.5=\sqrt (7X2.5-9)=\sqrt (17.5-9)=R.H.S$ Hence,$m=2.5$ is a valid solution