Question

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


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Answer 1

Let us say, first number be x and the second number is 27 – x.

Therefore, the product of two numbers

$x(27 – x) = 182$

$⇒ x²– 27x – 182 = 0$

$⇒ x² – 13x – 14x + 182 = 0$

$⇒ x(x – 13) -14(x – 13) = 0$

$⇒ (x – 13)(x -14) = 0$

Thus, either, $= -13 = 0$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

Hence, the numbers are 13 and 14.