Question
Two positive integers have HCF 12 and LCM 180. If the
sum of the two numbers is 96, what is the positive difference between them?Solution
ATQ, Let the numbers be a and b. a × b = HCF × LCM = 12 × 180 = 2160. a + b = 96. So a and b are roots of t² − 96t + 2160 = 0. Discriminant: Δ = 96² − 4×2160 = 9216 − 8640 = 576 ⇒ √Δ = 24. Roots: (96 ± 24)/2 ⇒ 60 and 36. Difference = 60 − 36 = 24.
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