Mathematics
Find two numbers whose sum is 27 and product is 182.
Quadratic Equations
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Answer
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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