Find the value of x2 - 7 if
\(\sqrt {5x + 16}\) + \(\sqrt {5x - 16}\) = \(\sqrt {41}\) + \(\sqrt {9}\).
Answer & explanation
Correct answer: option 2
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