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The difference of two number is 2 and their product is 224.Find the numbers.

Sagot :

misspancitcanton

Answer:

The numbers are 14 and 16.

Step-by-step explanation:

To find the two numbers with a difference of two and the product is 224, we need to construct the equation.

Let x be the larger number.

x - 2, the smaller number because they have a difference of 2.

Equation:

x (x - 2) = 224

Solution:

x (x - 2) = 224

x² - 2x = 224

x² - 2x - 224 = 0

Now, we ended up with a trinomial. To find the two numbers, we need to factor it.

Factoring Trinomials

Trinomial is a polynomial with three terms which are connected by plus or minus notations. It is expressed as a² + b + c.

To factor, we need to follow these steps:

1. Find the factors of "ac" that when combined it will result to "b".

2. When "c" is positive, the sign in each binomial is the same as "b".

3. When "c" is negative, the sign in each binomial is different.

4. Write as the product of two binomials ( )( ).

Let us continue.

x² - 2x - 224

(x - 16)(x + 14)

Therefore, x = 16 and x = -14.

Since we are looking for a positive value, we are going to use the positive value of x and that is 16.

Larger number is 16.

x - 2 = 16 - 2 = 14

Smaller number is 14.

Final Answer:

The two numbers are 14 and 16.

Checking:

x (x - 2) = 224

16 (16 - 2) = 224

16 (14) = 224

224 = 224 ✔

For the definition of factoring trinomial, visit the link:

https://brainly.ph/question/212278

For examples of factoring trinomial:

https://brainly.ph/question/170158

https://brainly.ph/question/1654743

#LetsStudy

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