Two numbers differ by 3 and their product is 504. Find the numbers.
Given, two numbers differ by 3.
Let one of the numbers be ‘a’.
Second number = a – 3
Also, their product is 504.
⇒ a(a – 3) = 504
⇒ a2 – 3a – 504 = 0
⇒ a2 – 24a + 21a – 504 = 0
⇒ a(a – 24) + 21(a – 24) = 0
⇒ (a + 21)(a – 24) = 0
⇒ a = -21, 24
Thus numbers are -21, -24 or 24, 21