Question

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

Answer 1

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Answer:

$13,14$

Step-by-step explanation:

By trial and error, we can conclude $13,14$ is the answer.

If you know quadratic equation in two unknowns, you can do this:

$x+y=27\\xy=182$

So sub. $x=27-y$ into the second equation.

$(27-y)y=182\\27y-y^2=182\\y^2-27y+182=0\\(y-13)(y-14)=0\\y=13,14$

If $y=13$, then $x=27-y=14$

If $y=14$, them $x=27-y=13$.

Answer 2

$\huge \underline \mathbb {SOLUTION:-}$

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, 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

• Hence, the numbers are 13 and 14.

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