Mathematics, 06.07.2019 07:00 mikey200059

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

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Answer from: dejaproctor17

A quadratic equation refers to an equation that can be rearranged into standard form $\rm ax^2 + bx + c = 0 \\\\$ .

Quadratic equation formed for the given question will be:

x^2 + 6x - 187 = 0

The answer obtained by solving the equation will be :

x = 11 and y = 17 .

How to form quadratic equation?

Let the two numbers be x and y.

Given:

Product of x and y is 187

Therefore, xy = 187 ... (1)

And difference between x and y is 6

Therefore, x + 6 = y ... (2)

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

$\begin{aligned}x(x+6) &= 187\\x^2 + 6x &= 187\\x^2 + 6x - 187 &= 0\end{aligned}$

How to solve quadratic equation?

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

x^2 + 6x - 187 = 0 .

Formula for solving quadratic equation:

$x = \dfrac{-b+\sqrt{b^2-4ac}}{2a}$

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

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

$\begin{aligned}x &= \dfrac{-6 \pm \sqrt{6^2 - 4(1)(-187)}}{2}\\\\&= \dfrac{-6\pm \sqrt{36+748} }{2} \\&= \dfrac{-6\pm \sqrt{784}}{2}\\&=\dfrac{-6 \pm 28}{2}\end{aligned}$

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

$\begin{aligned}x &= \dfrac{-6 + 28}{2}\\&= \frac{22}{2} \\&x=11\\\end{aligned}$

Therefore, as per equation 2

$\begin{aligned}x+6 = y\\11+6 &= y\\17 &= y \end{aligned}$

Hence, the natural numbers will be 11 and 17.

Learn more about quadratic equations here:

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Answer from: MadisonUpky9652

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.

Answer from: Quest

answer: it is d

step-by-step explanation:

Answer from: Quest

The answer would he -4,-2 because the points are just on the opposite side. since the x axis is +4 it's going to he -4 and since the y axis is -2 it stays there because whaen rotated it stays in the third quadrant
Hello! could someone with this problem?

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

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