The product of two natural numbers, one of which is greater than the other by 6, is 187. find these numbers.

A quadratic equation refers to an equation that can be rearranged into standard form   .

Quadratic equation formed for the given question will be:

The answer obtained by solving the equation will be :

and .

Let the two numbers be x and y.

Given:

Product of x and y is 187

Therefore,                        ...  (1)

And difference between x and y is 6

Therefore,                       ...  (2)

On substituting the value of y in equation 1 we get:

A quadratic equation can be solved by different methods such as factoring, formula method, etc.

Here we will be using formula to solve the equation

.

for the given equation, a = 1, b = 6 and c = -187

Putting the values of a, b and c in the formula we get:

Since, natural numbers cannot be negative, we will solve taking the addition sign.

Therefore, as per equation 2

Hence, the natural numbers will be 11 and 17.

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11,17

Step-by-step explanation:

First method:

factor 187 into 11*17, both of which are natural numbers, and difference is 6, so satisfies conditions for the answers.

Second method:

Product and difference: xy=p, x-y=6, half the difference is 3.

An approximation for the average between x and y can be found by taking the square root of the product p = 187

sqrt(187)=13.7, so we can try (14-3)(14+3) = 11*17=187.

Note: since sqrt(187) is always less than x*y, we try the next greater natural number (14) to start.