Question

The difference of two natural number is 5 and their difference of their reciprocal is 1/10.find the number.

Answer 1

Let the two numbers be x and x - 5 .

According to the question.

⇒ x(x-5) = 50

⇒ x2 - 5x - 50 = 0

⇒ x2 - 10x + 5x - 50 = 0

⇒ x (x - 10) + 5 (x - 10) = 0

⇒ (x+5) (x-10) = 0

⇒ (x+5) (x-10) = 0

⇒ x = -5 or 10

⇒ x = 10 (x = -5 , rejected)

∴ Two numbers are 10 and (10-5) = 5.

Answer 2

Let the first natural no be x

second will be y

then ac to artist

x-y =5____--_______(1)

and again 1/x-1/y=1/10_________2)

x-y/x●y=1/10

xy=5

now,

x-y=50___-_(1)

x+y=√(x-y)^2+4xy

x+y=5^2+50*4

x+y=√225_---;--;----(3)

x+y=+-15

from 1 and 3 each other.

x-y=5

x+y=-15 if it is negative

_____

2x=10

x=5

and y=10

and.if it is -15

then

x-y=5

x+y=15

_____

2x=20

x=10

and y=5ans