Find the value of x² - 7 if

\(\sqrt {5x + 16}\) + \(\sqrt {5x - 16}\) = \(\sqrt {41}\) + \(\sqrt {9}\).

18

We can easily see that x = 5 will satisfy the expression:

⇒ \(\sqrt {5x + 16}\) + \(\sqrt {5x - 16}\) = \(\sqrt {41}\) + \(\sqrt {9}\)

⇒ \(\sqrt {25 + 16}\) + \(\sqrt {25 - 16}\) = \(\sqrt {41}\) + \(\sqrt {9}\)

⇒ \(\sqrt {41}\) + \(\sqrt {9}\) = \(\sqrt {41}\) + \(\sqrt {9}\)

Hence,

x² - 7 = 5² - 7 = 25 - 7 = 18