There are 3 different numbers.The sum of the number is 19.The greatest number is equal to the product of the other two numbers.what is the smallest number
Let the numbers be a, b, and c where c is the largest
a+b+c=19
c=ab
a+b+ab=19
a(1+b) = (19 - b)/(1 + b)
did not mean to post yet,working on a silly tablet
a = (19-b)/(1+b)
No unique solution.
Eg. If b=1, a=9, c=9
If b=2, a = 17/3 , c = 34/3
etc
To find the smallest number, let's first assign variables to the three numbers. Let's call the smallest number x, the middle number y, and the greatest number z.
According to the given information, we know the following:
1) The sum of the numbers is 19, which can be written as x + y + z = 19.
2) The greatest number is equal to the product of the other two numbers, meaning z = xy.
Now we can use these equations to solve for the smallest number x.
Substituting z = xy into the sum equation, we get:
x + y + xy = 19.
Rearranging this equation, we have:
x + xy + y = 19.
Factoring out x from the first two terms, we get:
x(1 + y) + y = 19.
To isolate x, we subtract y from both sides:
x(1 + y) = 19 - y.
Dividing both sides by (1 + y), we find:
x = (19 - y)/(1 + y).
Now that we have an equation for x, we can determine the possible values for x given the constraints. Since we are looking for the smallest value, we need to consider the smallest possible value for y.
Note that y and x cannot be zero, as one number must be the greatest and cannot be equal to the sum of the other two numbers.
Let's select y = 1, which represents the smallest possible value for y.
Plugging y = 1 into the equation for x, we get:
x = (19 - 1)/(1 + 1) = 18/2 = 9.
Therefore, the smallest number is 9.