Mathematics

Let a and b be two non-zero rational numbers such that $a + \dfrac{1}{b} = 0$ . Without assigning any numerical values, determine whether ab is positive or negative. Justify your answer.

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Given:

⇒ $a + \dfrac{1}{b} = 0$

⇒ $a = -\dfrac{1}{b}$

Multiplying both sides by b :

$\Rightarrow ab = -\dfrac{1}{b} \times b \\[1em] \Rightarrow ab = -1.$

Since ab = -1, the product ab is negative.

Hence, ab is negative.

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