Answer:Let's call the two numbers x and y. We know that:
xy = 72
x + y = -38
We can use the first equation to solve for one of the variables in terms of the other:
x = 72/y
Then, we can substitute this expression into the second equation:
72/y + y = -38
y^2 + 72 = 38y
y^2 - 38y + 72 = 0
This is a quadratic equation that can be solved using the quadratic formula:
y = (-b ± √(b^2 - 4ac)) / 2a
where a = 1, b = -38, c = 72.
Plugging in these values, we get:
y = (38 ± √(38^2 - 4(1)(72))) / 2(1)
y = (38 ± √(1444)) / 2
y = (38 ± 38) / 2
So, we have two solutions for y:
y = 38 / 2 = 19
y = -38 / 2 = -19
With either of these values for y, we can use the first equation to solve for x:
x = 72/y = 72/19 = 3.8
or
x = 72/-19 = -3.8
So, the two numbers whose product is 72 and whose sum is -38 are x = 3.8 and y = 19, or x = -3.8 and y = -19.
Explanation:
Let's call the two numbers x and y. We know that:
xy = 72
x + y = -38
We can use the first equation to solve for one of the variables in terms of the other:
x = 72/y
Then, we can substitute this expression into the second equation:
72/y + y = -38
y^2 + 72 = 38y
y^2 - 38y + 72 = 0
This is a quadratic equation that can be solved using the quadratic formula:
y = (-b ± √(b^2 - 4ac)) / 2a
where a = 1, b = -38, c = 72.
Plugging in these values, we get:
y = (38 ± √(38^2 - 4(1)(72))) / 2(1)
y = (38 ± √(1444)) / 2
y = (38 ± 38) / 2
So, we have two solutions for y:
y = 38 / 2 = 19
y = -38 / 2 = -19
With either of these values for y, we can use the first equation to solve for x:
x = 72/y = 72/19 = 3.8
or
x = 72/-19 = -3.8
So, the two numbers whose product is 72 and whose sum is -38 are x = 3.8 and y = 19, or x = -3.8 and y = -19.