JAMB - Mathematics (2006 - No. 38)
A binary operation * on the set of rational numbers is defined as \(x \ast y = \frac{x^2 - y^2}{2xy}\). Find \(-5 \ast 3\)
\(\frac{-8}{15}\)
\(\frac{8}{15}\)
\(\frac{17}{15}\)
\(\frac{-17}{15}\)
Explanation
\(x \ast y = \frac{x^2 - y^2}{2xy}\)
=\(\frac{(x+y)(x-y)}{2xy}\)
-5 \(\ast 3 =\frac{(-5+3)(-5-3)}{2(-5\times3)}\)
=\(\frac{-2 \times -8}{2(-5\times3)}\)
=\(\frac{-8}{15}\)
=\(\frac{(x+y)(x-y)}{2xy}\)
-5 \(\ast 3 =\frac{(-5+3)(-5-3)}{2(-5\times3)}\)
=\(\frac{-2 \times -8}{2(-5\times3)}\)
=\(\frac{-8}{15}\)
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