A binary operation * is defined on the set of real numbers, by (a * b = frac{a}{b} + frac{b}{a}). If ((sqrt{x} + 1) * (sqrt{x} – 1) = 4), find the value of x.
-
A.
6 -
B.
5 -
C.
4 -
D.
3
Correct Answer: Option D
Explanation
((sqrt{x} + 1) * (sqrt{x} – 1) = 4 implies frac{sqrt{x} + 1}{sqrt{x} – 1} + frac{sqrt{x} – 1}{sqrt{x} + 1} = 4)
(frac{(sqrt{x} + 1)(sqrt{x} + 1) + (sqrt{x} – 1)(sqrt{x} – 1)}{(sqrt{x} – 1)(sqrt{x} + 1)})
= (frac{x + 2sqrt{x} + 1 + x – 2sqrt{x} + 1}{x – 1} implies frac{2x + 2}{x – 1} = 4)
(2x + 2 = 4x – 4 therefore 4x – 2x = 2x = 2 + 4= 6)
(x = 3)