Question

If $a$ is between 0 and 1, which of the following statements is (are) true? (i) $a^2 - 1 > 0$ (ii) $a^2 + 1 > 0$ (iii) $a^2 - a > 0$

Accepted Answer

A. Since $0 < a < 1$: 1. $0 < a^2 < 1 \implies a^2 - 1 < 0$ (False) 2. $1 < a^2 + 1 < 2 \implies a^2 + 1 > 0$ (True) 3. $a^2 < a \implies a^2 - a < 0$ (False) Thus, only statement (ii) is true.

Inequalities for a fraction between 0 and 1

Explanation

Practise this under exam conditions