Equation is 5x² - 2x - 72 = 0 and the two integers are 4 and 18
Step-by-step explanation:
- Step 1: Let one number be x. Then the other is 5x - 2. Product = 72
⇒ 72 = x(5x - 2)
⇒ 72 = 5x² - 2x
⇒ 5x² - 2x - 72 = 0 is the equation
x = 2 ± √4 - 4 × 5 × -72/2 × 5 (Using quadratic formula)
x = 2 ± √4 + 1440/10
x = 2 ± 38/10
= 40/10, -36/10 (negative decimal value is neglected)
∴ x = 4
5x - 2 = 20 - 2 = 18
