Question

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

Answer 1

Answer:

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

Answer 2

Answer:

Hello,

x=4 or x=12

Step-by-step explanation:

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