Two numbers differ by 4 and their product is 192. Find the numbers.
Given, two numbers differ by 4.
Let one of the numbers be ‘a’.
Second number = a – 4
Also, their product is 192.
⇒ a(a – 4) = 192
⇒ a2 – 4a – 192 = 0
⇒ a2 – 16a + 12a – 192 = 0
⇒ a(a – 16) + 12(a – 16) = 0
⇒ (a + 12)(a – 16) = 0
⇒ a = -12, 16
Thus numbers are -12, -16 or 12, 16