Question

The sum of two numbers is 3 and their product is 54. Find these numbers

Answer 1

Answer:

The two numbers are 9 and 6.

Step-by-step explanation:

Let the two numbers be x and y.

According to the question, x−y=3…(i)

Also, x×y=54

⇒x=

y

54

…(ii)

On putting the value of x=

y

54

in Eq. (i), we get

y

54

−y=3

⇒54−y

2

=3y

⇒y

2

+3y−54=0

⇒y

2

+9y−6y−54=0

⇒y(y+9)−6(y+9)=0

⇒(y−6)(y+9)=0

⇒y=−9 and 6

But y=−9 can't be the one number as it is given that the numbers are positive.

⇒y=6, then x=

6

54

=9

Hence the two numbers are 9 and 6.