Question

Write a pair of integers whose product is – 36 and whose difference is 15.

Answer 1

Chris sonication sickish just 20 words

Answer 2

Answer:

The pair of integers are  x=3 and y=-12 or x=12 and y=-3 whose product is -36 and their difference will be 15.

To find:

The values of the integers pair which has their product and difference as -36 and 15.

Solution:

Assume x and y are the integers

Given that their product is -36

$xy=-36\\\\y= \frac {(-36)}{x}$

Their difference is 15.

$x-y=15$

Substitute y value in the above equation

$\begin{array} { l } { x - \frac { - 36 } { x } = 15 } \\\\ { \frac { x ^ { 2 } + 36 } { x } = 15 } \end{array}$

$\begin{array} { l } { x ^ { 2 } + 36 = 15 \mathrm { x } } \\\\ { \mathrm { x } ^ { 2 } - 15 \mathrm { x } + 36 = 0 } \\\\ { \mathrm { x } ^ { 2 } - 12 \mathrm { x } - 3 \mathrm { x } + 36 = 0 } \\\\ { \mathrm { x } ( \mathrm { x } - 12 ) - 3 ( \mathrm { x } - 12 ) = 0 } \\\\ { ( \mathrm { x } - 3 ) ( \mathrm { x } - 12 ) = 0 } \\\\ { \mathrm { x } = 3 \text { and } \mathrm { x } = 12 } \end{array}$

Substitute the values of x in y

$\begin{array} { l } { \mathrm { y } = \frac { - 36 } { \mathrm { x } } } \\\\ { \mathrm { y } = \frac { - 36 } { 3 } } \\\\ { \mathrm { y } = - 12 } \\\\ { \mathrm { y } = \frac { - 36 } { 12 } } \\\\ { \mathrm { y } = - 3 } \end{array}$

Hence, the values of the integers pair are

$\begin{array} { l } { x = 12 \text { and } y = - 3 } \\\\ { x = 3 \text { and } y = - 12 } \end{array}$