Respuesta :
Answer:
[tex]x = -22[/tex]
Step-by-step explanation:
The formula for calculating the distance between two integers x and y is:
[tex]| y-x | = d[/tex]
Where d is the difference between the two numbers and x is the smallest integer
In this case we know that [tex]d = 8[/tex] then:
[tex]| y-x | = 8[/tex]
We also know that the product of both numbers is equal to 308.
This means that:
[tex]xy = 308[/tex]
We know that [tex]x <y[/tex] and that [tex]x <0[/tex] and [tex]y <0[/tex]
then the difference of [tex]y-x[/tex] will always be positive, for this reason we can eliminate the absolute value of the first equation and we have that:
[tex]y-x = 8[/tex]
and
[tex]xy = 308[/tex]
We substitute the first equation in the second equation:
[tex]x (x + 8) = 308[/tex]
Now we solve for x:
[tex]x ^ 2 + 8x -308 = 0[/tex]
To factor the equation, you must look for two numbers that, by multiplying them, you get as a result -308 and by adding these numbers you get as a result 8.
These numbers are 22 and -14
Then the equation is as follows:
[tex](x + 22) (x-14) = 0[/tex]
The solutions are:
[tex]x = -22[/tex], and [tex]x = 14[/tex]
As we know that [tex]x <0[/tex] then we take the negative solution [tex]x = -22[/tex]
Finally we find the value of y.
[tex]y -(-22) = 8[/tex]
[tex]y = -22 + 8[/tex]
[tex]y = -14[/tex]
Answer:
Integer are (-14) and (-22). The smallest integer is (-22).
Step-by-step explanation:
Let the integer be (-x) and (-y)
(-y) - (-x) = 8 (x here is a smaller integer)
-x = b, -y = a
a - b = 8...(1)
(-a)(-b) = 308..(2)
Putting value of ab from (2) in (1):
[tex]a=\frac{308}{b}[/tex]
[tex]\frac{308}{b}-b=8[/tex]
[tex]b^2-8b-308[/tex]
[tex]b=-14,22[/tex]
[tex]b=-x[/tex]
[tex]-14=-x[/tex] (b=-14)
x = 14 (reject, integer asked are negative)
[tex]b=-x[/tex]
[tex]22=-x[/tex] (b=22)
x = -22
[tex]a=\frac{308}{b}=\frac{308}{22}=14[/tex]
[tex]a=14=-y[/tex]
y = -14
Integer are (-14) and (-22). The smallest integer is (-22).
