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 \(-3 \Delta -1\).
- \(-4\sqrt{3}\)
-
\(\frac{-4\sqrt{3}}{3}\)
- \(\frac{-3\sqrt{3}}{4}\)
- \(\frac{-3\sqrt{3}}{4}\)
The correct answer is: B
Explanation
\(a \Delta b\) = \(\frac{a+b}{\sqrt{ab}}\)
\(-3\Delta -1\) = \(\frac{-3 + -1}{\sqrt{-3\times -1}}\)
\(\frac{-4}{\sqrt{3}}\), rationalising, we have
\(\frac{-4 \times \sqrt{3}}{\sqrt{3}\times \sqrt{3}} = \frac{-4\sqrt{3}}{3}\)