Find the value of x if \(\sqrt{x - y} =2\) and \(\sqrt{x + y} = \sqrt{14}\)

Explanation:

∵ \(\sqrt{x - y} =2\) ............................ (1)

And \(\sqrt{x + y} = \sqrt{14}\) ................... (2)

Square both equations:

\((\sqrt{x - y})^2 =2^2\)

⇒ x - y = 4 .................................. (3)

And \((\sqrt{x + y})^2 = (\sqrt{14})^2\)

⇒ x + y = 14 ............................... (4)

On adding equations (3) and (4), we get:

2x = 18

⇒ x = 9

Putting the value of x in equation (4), we get:

9 + y = 14

⇒ y = 5