A binary operation * on the set of rational numbers is defined as \(x \times y = \frac{x^2-y^2}{2xy}\) find \(-5 \times 3\)
Question 1 Report
A binary operation * on the set of rational numbers is defined as \(x \times y = \frac{x^2-y^2}{2xy}\) find \(-5 \times 3\)
Answer Details
To evaluate -5 * 3 using the binary operation * on the set of rational numbers, we substitute x = -5 and y = 3 in the given expression:
-5 * 3 = (-5)^2 - 3^2 / 2(-5)(3)
Simplifying the numerator, we get:
(-5)^2 - 3^2 = 25 - 9 = 16
Simplifying the denominator, we get:
2(-5)(3) = -30
Substituting these values back into the expression, we get:
-5 * 3 = 16 / -30
Simplifying the fraction, we get:
-5 * 3 = -8/15
Therefore, the value of -5 * 3 using the binary operation * on the set of rational numbers is -8/15.
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