Question
The product of two positive integers is 3630. If their
HCF is 11 and their sum is 143, then find the difference between the numbers.Solution
Let the numbers be 11a and 11b
Then:
11a × 11b = 3630 ⇒ ab = 30 ...............(1)
11a + 11b = 143 ⇒ a + b = 13
Put a = (13 - b) in (1):
(13 - b) × b = 30
⇒ 13b - b² = 30
⇒ b² - 13b + 30 = 0
⇒ b² - 3b - 10b + 30 = 0
⇒ b(b - 3) - 10(b - 3) = 0
⇒ (b - 3)(b - 10) = 0
So, b = 3 or 10
Then, numbers are 33 and 110
Required difference = 77
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