Answer:
It differs by 4
16 - 12 = 4
4 = 4
Their product is 192
(16) (12) = 192
192 = 192
Step-by-step explanation: The sum of two numbers is 60 and their product is 576. Find the numbers. Let x and y are the two consecutive integers
The sum of two numbers is 60
x + y = 60 ---- (1)
Product of two numbers = 576
xy = 576
y = 576/x ----- (2)
Now we apply the value of x in (1)
x + (576/x) = 60
(x2 + 576) / x = 60
x2 + 576 = 60x
x2 - 60x + 576 = 0
(x - 12) (x - 48) = 0
x - 12 = 0
x = 12
If x = 12
y = 576 / 12
y = 48
x - 48 = 0
x = 48
If x = 48
y = 576 / 48
y = 12
So the required integers are 18 and The sum of two numbers is 60
48 + 18 = 60
60 = 60
The product is 576
48 (18) = 576
576 = 57648.
Two positive numbers differ by 4 and their product is 192. Find the numbers.
Let x and y be two positive numbers
It differs by 4
x - y = 4
x = 4 + y --- (1)
Their product is 192
xy = 192
y = 192/x --- (2)
By applying the value of y in (1), we get
x = 4 + (192/x)
x = (4x + 192)/x
x2 = 4x + 192
x2 - 4 x - 192 = 0
(x - 16) (x + 12) = 0
x - 16 = 0
x = 16
x + 12 = 0
x = -12
If x = 16
Then,
y = 192/16
y = 12
Since it is positive number we have to choose 16 for x.
