Question

Find two positive number which have a difference of five whose product is 84.

Answer 1

Answer:

The required two positive numbers are 7 & 12.

Step-by-step-explanation:

Let the greater positive number be x.

And the smaller positive number be y.

From the first condition,

The difference between the two numbers is 5.

x - y = 5

⇒ x = 5 + y

⇒ x = y + 5 - - - ( 1 )

From the second condition,

The product of two numbers is 84.

xy = 84

⇒ ( y + 5 ) * y = 84 - - - [ From ( 1 ) ]

⇒ y² + 5y = 84

⇒ y² + 5y - 84 = 0

⇒ y² + 12y - 7y - 84 = 0

⇒ y ( y + 12 ) - 7 ( y + 12 ) = 0

⇒ ( y + 12 ) ( y - 7 ) = 0

⇒ ( y + 12 ) = 0 OR ( y - 7 ) = 0

⇒ y + 12 = 0 OR y - 7 = 0

⇒ y = - 12 OR y = 7

As the number is positive, y = - 12 is unacceptable.

y = 7

∴ Smaller number = 7

By substituting y = 7 in equation ( 1 ), we get,

x = y + 5 - - - ( 1 )

⇒ x = 7 + 5

⇒ x = 12

∴ Greater number = 12

∴ The required two positive numbers are 7 & 12.