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 ...

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 \(-3 \Delta -1\).

Answer Details

To evaluate \(-3 \Delta -1\), we simply need to substitute a = -3 and b = -1 in the definition of the binary operation: \(-3 \Delta -1 = \frac{-3+(-1)}{\sqrt{(-3)(-1)}} = \frac{-4}{\sqrt{3}}\) To simplify this expression, we rationalize the denominator by multiplying both the numerator and denominator by \(\sqrt{3}\): \(\frac{-4}{\sqrt{3}} = \frac{-4}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{-4\sqrt{3}}{3}\) Therefore, the correct answer is.