the sum of 2 numbers is 17 and their product is 66
Answers
The two numbers are 11 and 6
Step-by-step explanation:
Let the numbers be x and y. Then according to the condition
x + y = 17 ...... eq (1)
xy =66 ........ eq (2)
From equation (2), we have
x = 66/y
Substituting the value of x in eq (1)
66/y + y = 17
(66 + y2 )/y= 17
66 + y2 = 17y
y2 -17y +66 = 0
Now, we need to factorize the it
y2 -11y -6y +66 = 0
y(y-11) -6 (y-11) = 0
(y-11)(y-6)=0
This shows,
y = 11,6
The complete question is:
The sum of 2 numbers is 17 and their product is 66. Find the two numbers.
Given:
Sum of 2 numbers= 17
Product of 2 numbers= 66
To find:
The two numbers
Solution:
Let the two numbers be x and y
So, we can write:
x+y= 17 --------equation 1
x×y = 66 --------equation 2
From equation 2, we get x= 66/y
We place it in equation 1:
66/y + y = 17
On solving, we get a quadratic equation as:
y2 -17y +66 = 0
Now, solving the quadratic equation:
y2 -17y +66 = 0
or, y2 -11y-6y +66 = 0
or, y(y-11) -6 (y-11) = 0
or, (y-11) (y-6)=0
So, y = 11, 6
Since we have two values of y, we place them in equation 1 individually to find the value of x.
x+y= 17
So, the value of x is 11 or 6.