Chapter 10 - Radical Expressions and Equations - 10-4 Solving Radical Equations - Practice and Problem-Solving Exercises - Page 623: 19

$x=4.5$

$Given,$$\sqrt(3x+1)=\sqrt(5x-8)$ Squaring,we get: $3x+1=5x-8$ $3x+1+8=5x-8+8$ $3x+9=5x$ $2x=9$ $x=9\div2=4.5$ We need to check by putting the obtained value in the original equation : $L.H.S=\sqrt (3X4.5+1)=\sqrt 14.5$ $R.H.S=\sqrt (5X4.5-8)=\sqrt (22.5-8)=\sqrt 14.5$ $L.H.S=R.H.S$ ,Hence,$x=4.5$ is a valid solution