Question

the sum of two numbers is 27 and it's product is 182. find those numbers​

Answer 1

Step-by-step explanation:

Let the first number be x then the second number will be 27−x.

x(27-x)=182

⇒27x−x

2

=182

⇒x

2

−27x+182=0

⇒x

2

−13x−14x+182=0

⇒x(x−13)−14(x−13)=0

⇒(x−14)(x−13)=0

⇒x=14,13

If the first number is 14, then the second number is 13 and if the first number is 13, then the second number is 14.

Answer 2

Answer:

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Let the first number be x

Thus the second number can be represented as 27 - x

Since the product of two numbers is 182.

$x(27 - x) = 182 \\ 27x - {x}^{2} - 182 = 0 \\ {x}^{2} - 27x + 182 = 0$

Splitting -27 x as -13x -14x

${x}^{2} - 13x - 14x + 182 = 0 \\ x(x - 13) - 14(x - 13) =0 \\ (x - 13)(x - 14) = 0$

The roots of this equation are the values of x for which (x-13)(x-14) = 0

which are,

x - 14 = 0 or x - 13 = 0

Thus , x = 13 or x = 14

If the first number is 14, the second number will be 27 - 14 = 13

If the first number is 13, the second number will be 27 - 13 = 14

Thus, the two numbers are 13 & 14.