Mathematics 2009 JAMB Past Questions - Question 16: Determine the value of x for which (x² -1) >0

Correct Answer

A

Explanation

x (x-1) > 0x > 0 or x > 1To determine the value of x for which (x² - 1) > 0, we need to find the values of x that make the expression greater than zero.First, let's factor the expression:(x² - 1) = (x - 1)(x + 1)Now, we can analyze the sign of each factor:(x - 1) > 0 when x > 1(x + 1) > 0 when x > -1To satisfy the condition (x² - 1) > 0, both factors must be greater than zero. Therefore, we need x to be greater than 1 and greater than -1.In interval notation, the solution is x ∈ (-∞, -1) ∪ (1, +∞). This means that any value of x that is less than -1 or greater than 1 will make the expression (x² - 1) greater than zeroTo determine the value of x for which (x² - 1) > 0, we need to find the values of x that make the expression greater than zero.First, let's factor the expression:(x² - 1) = (x - 1)(x + 1)Now, we can analyze the sign of each factor:(x - 1) > 0 when x > 1(x + 1) > 0 when x > -1To satisfy the condition (x² - 1) > 0, we need either both factors to be greater than zero or both factors to be less than zero.When x > 1, both factors are greater than zero, so (x² - 1) > 0.When x < -1, both factors are less than zero, so (x² - 1) > 0.Therefore, the solution is x ∈ (-∞, -1) ∪ (1, +∞). This means that any value of x that is less than -1 or greater than 1 will make the expression (x² - 1) greater than zero.