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

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

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5968 Points
one year ago
Dear Student

Let us say,
first number be x and the second number is 27 - x.
Therefore, the product of two numbers x(27 - x) = 182
⇒ x^2 – 27x - 182 = 0
⇒ x^2 – 13x - 14x + 182 = 0
⇒ x(x - 13) -14(x - 13) = 0
⇒ (x - 13)(x -14) = 0
Thus, either, x = -13 = 0 or x - 14 = 0
⇒ x = 13 or x = 14
Therefore, if first number = 13, then second number = 27 - 13 = 14
And if first number = 14, then second number = 27 - 14 = 13
Thus, the numbers are 13 and 14

Thanks

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