Question

A binary operation \(\Delta\) is defined on the set of real numbers, R, by \(a \Delta b=\frac{a+b}{\sqrt{a b}}\), where \(a \neq 0, b \neq 0\). Evaluate \(-3 \Delta-1\)

A. \(-4 \sqrt{3}\)
B. \(\frac{-4 \sqrt{3}}{3}\)
C. \(\frac{-3 \sqrt{3}}{4}\)
D. \(\frac{-3 \sqrt{3}}{4}\)

Answer 1

Correct Answer:

Option B

Explanation
\[
\begin{aligned}
&a \Delta b=\frac{a+b}{\sqrt{a b}} \\
&-3 \Delta-1=\frac{-3+-1}{\sqrt{-3 \times-1}}
\end{aligned}
\]
\(\frac{4}{\sqrt{3}}\), rationalising, we have
\[
\frac{-4 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}=\frac{-4 \sqrt{3}}{3}
\]