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 \(-4\sqrt{3}\)
  • B \(\frac{-4\sqrt{3}}{3}\)
  • C \(\frac{-3\sqrt{3}}{4}\)
  • D \(\frac{-3\sqrt{3}}{4}\)
waec 2017furthermathematics

The correct answer is B. \(\frac{-4\sqrt{3}}{3}\)

\(a \Delta b\) = \(\frac{a+b}{\sqrt{ab}}\)

\(-3\Delta -1\) = \(\frac{-3 + -1}{\sqrt{-3\times -1}}\)

\(\frac{-4}{\sqrt{3}}\), rationalising, we have

\(\frac{-4 \times \sqrt{3}}{\sqrt{3}\times \sqrt{3}} = \frac{-4\sqrt{3}}{3}\)

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