Question

the sum of 2 numbers is 17 and their product is 66

Answer 1

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

Answer 2

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.

Therefore, the two numbers are 6 and 11.