A binary operation (Delta) is defined on the set of real numbers, R, by (a Delta b = frac{a+b}{sqrt{ab}}), where a(neq) 0, b(neq) 0. Evaluate (-3 Delta -1).
-
A.
(-4sqrt{3}) -
B.
(frac{-4sqrt{3}}{3}) -
C.
(frac{-3sqrt{3}}{4}) -
D.
(frac{-3sqrt{3}}{4})
Correct Answer: Option B
Explanation
(a Delta b) = (frac{a+b}{sqrt{ab}})
(-3Delta -1) = (frac{-3 + -1}{sqrt{-3times -1}})
(frac{-4}{sqrt{3}}), rationalising, we have
(frac{-4 times sqrt{3}}{sqrt{3}times sqrt{3}} = frac{-4sqrt{3}}{3})