Question

PLEASE HELP
How to solve radical equations

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

Possible Answers:
-11, 0, 2, 3, 5, 8, 11, 16, 100, or no possible solution

Answer 1

Answer:

3,11

Step-by-step explanation:

$\sqrt{2x+3}=2+\sqrt{x-2}\\  squaring\\2x+3=4+x-2+4\sqrt{x-2} \\2x+3-4-x+2=4\sqrt{x-2} \\x+1=4\sqrt{x-2 }\\again~squaring\\x^{2}+2x+1=16(x-2)\\x^{2}+2x-16 x+1+32=0\\x^2-14 x+33=0\\x^2-3x-11x+33=0\\x(x-3)-11(x-3)=0\\(x-3)(x-11)=0\\x=3,11$