How to Solve Radical Equations Using Conguate Radicals 

Another method. Let the two radicals be an and b respectively. Then a-b=2 and a^2-b^2=12. Or (a+b)(a-b)=12. Substituting and solving you get a=4 Substituting in the first radical for a you get x value as 9. Could do it in the head.

Nice sol

How to Solve Radical Equations: √(x + 7) - √(x - 5) = 2; x = ? First method: √(x + 7) - √(x - 5) = 2 = 4 - 2 = √16 - √4 = √(9 + 7) - √(9 - 5); x = 9 Second method: √(x + 7) = √(x - 5) + 2, x + 7 = [√(x - 5) + 2]² = x - 5 + 4√(x - 5) + 4, 4√(x - 5) = 8 √(x - 5) = 2, x - 5 = 2² = 4; x = 9 Answer check: x = 9, √(x + 7) - √(x - 5) = 2; Confirmed in First method Final answer: x = 9

X=9