Question

The sum of two integers is -12
. Their product is 36
. Find the numbers

Answer 1

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

Given :

Sum of two integers is -12

their product is 36

To Find

The numbers

Let the first integer be 'x'

another integer be 'y'

According to the question:-

$\bold{=>x+y=-12.......(1)}$

$\bold{=>xy=36.........(2)}$

$\bold{\green{= > x = \frac{36}{y} .......(3)}}$

Substitute value of 'x' from equation (3) into equation (1)

$= > \frac{36}{y} + y = - 12$

$= > \frac{36 + {y}^{2} }{y} = - 12$

$= > 36 + {y}^{2} = - 12y$

$= > {y}^{2} + 12y + 36$

$= > {y}^{2} + 6y + 6y + 36 = 0$

$= > y(y + 6) + 6(y + 6) = 0$

$= > (y + 6)(y + 6) = 0$

Now we get $\bold{\red{ y=-6}}$

Substitute y's value in equation (1)

$= > x + {\red{y}} = - 12$

$= > x{\red{ - 6 }}= - 12$

$= > x = - 12 + 6 = - 6$

$\huge\bold{\boxed{\purple{x=-6}}}$

$\huge\bold{\boxed{\purple{y=-6}}}$

$\huge\mathbb{check}$

$= > x + y = - 12$

$= > - 6 - 6 = - 12$

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

Given :

Sum of two integers is -12

their product is 36

To Find

The numbers

Let the first integer be 'x'

another integer be 'y'

According to the question:-

$\bold{=>x+y=-12.......(1)}$

$\bold{=>xy=36.........(2)}$

$\bold{\green{= > x = \frac{36}{y} .......(3)}}$

Substitute value of 'x' from equation (3) into equation (1)

$= > \frac{36}{y} + y = - 12$

$= > \frac{36 + {y}^{2} }{y} = - 12$

$= > 36 + {y}^{2} = - 12y$

$= > {y}^{2} + 12y + 36$

$= > {y}^{2} + 6y + 6y + 36 = 0$

$= > y(y + 6) + 6(y + 6) = 0$

$= > (y + 6)(y + 6) = 0$

Now we get $\bold{\red{ y=-6}}$

Substitute y's value in equation (1)

$= > x + {\red{y}} = - 12$

$= > x{\red{ - 6 }}= - 12$

$= > x = - 12 + 6 = - 6$

$\huge\bold{\boxed{\purple{x=-6}}}$

$\huge\bold{\boxed{\purple{y=-6}}}$

$\huge\mathbb{check}$

$= > x + y = - 12$

$= > - 6 - 6 = - 12$