Question

\sqrt{2x+1} = 2+\sqrt{x-3}

Answer 1

Hello,

x=4 or x=12

Explanation:

`√(2x+1) =2+√(x-3) \\\\2x+1=4+4√(x-3) +(x-3)\\\\2x+1-x+3-4=4√(x-3) \\\\x=4√(x-3) \\\\ x^2-16x+48=0\\\\\Delta=16^2-4*48=64=8^2\\\\x=(16-8)/(2) \ or x=(16+8)/(2)\\\\x=4 \ or\ x=12\\\\Since \ we\ have \ squared \ we\ must\ verify\ the \ solutions\ found:\\\\x=4 \Longrightarrow √(2*4+1) =? 2+√(4-3) \Longrightarrow 3 =? 2+1 \\\\x=12 \Longrightarrow √(2*12+1) =? 2+√(12-3) \Longrightarrow 5 =? 2+3 \\\\`

Answer 2

Square both sides

√(2x+1)=2+√(x-3)

or, 2x+1=(2+√(x-3))²

solving it you'll get two values of x, which are,

x = 4 and x = 12