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Question
The sum of two numbers is 48 and their product is 432. Find the numbers?
Solution
Given the sum of two numbers is 48
Let the two numbers be x and 48 – x also given their product is 432.
Hence x(48 - x) = 432
⇒ 48x - x2 = 432
⇒ 48x - x2 - 432 = 0
⇒ 𝑥2 - 48𝑥 + 432 = 0
⇒ 𝑥2 - 36𝑥 - 12𝑥 + 432 = 0 [By method of factorisation]
⇒ 𝑥(𝑥 - 36) - 12(𝑥 - 36) = 0
⇒ (𝑥 - 36)(𝑥 - 12) = 0
⇒ x = 36 or x = 12
∴ The two numbers are 12, 36.
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