Question

The difference of two integers is 1. The product of the integers is 30. What
are the integers?

Answer 1

`\large\underline{\bf \red{Step \:by\: Step \:Explanation:}}`

Let us take ,

• First integer be x .
• Second integer be y .

Also let us consider x > y .

According to first Condition :-

⇒ x - y = 1.

⇒ x = y + 1. .............(i)

According to second Condition :-

⇒ x × y = 30 .

⇒ ( y + 1 )y = 30 . [ From (i) ]

⇒ y² + y = 30.

⇒ y² + y - 30 = 0 .

⇒ y² + 6y - 5y -30 = 0.

⇒ y ( y + 6 ) -5 ( y + 6 ) = 0 .

⇒ ( y + 6 ) ( y - 5 ) = 0 .

`\red{\bf \longmapsto y = 5 , (-6)}`

Here y can sustain both values 5 and minus 6 as y is an integer.

So , x = -6 , 5 .

Hence possible answers are ,

`\boxed{\purple{\bf x = -6 , y = -5 }}`

`\qquad\qquad\qquad \bf Or`

`\boxed{\purple{\bf x = 6 , y = 5 }}`

.