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almond37 [142]
3 years ago
9

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

Mathematics
1 answer:
NemiM [27]3 years ago
4 0

\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 .

<u>Acco</u><u>rding</u><u> to</u><u> </u><u>first</u><u> </u><u>Condition</u><u> </u><u>:</u><u>-</u>

⇒ x - y = 1.

⇒ x = y + 1. .............(i)

<u>Acco</u><u>rding</u><u> to</u><u> </u><u>seco</u><u>nd</u><u> </u><u>Condition</u><u> </u><u>:</u><u>-</u>

⇒ 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 }}

.

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