Mathematics

Find two numbers whose sum is 27 and product is 182.

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Let first number be x and second number = (27 - x).

Given,

Product = 182

∴ x(27 - x) = 182

⇒ 27x - x² = 182

⇒ x² - 27x + 182 = 0

⇒ x² -13x - 14x + 182 = 0

⇒ x(x - 13) - 14(x - 13) = 0

⇒ (x - 14)(x - 13) = 0

⇒ x - 14 = 0 or x - 13 = 0

⇒ x = 14 or x = 13.

Hence, numbers are 13 and 14.

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