Question

The difference of two numbers is 5 and the difference of their reciprocals

is 1

10

. Find the numbers​

Answer 1

Answer:

Step-by-step explanation:

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 two numbers x, x+5

1/x-1/x+5=1/10

x+5-x/x(x+5)=1/10

5/x(x+5)=1/10

5×10=x(x+5)

50=x^2+5x

x^2+5x-50=0

(x-10)(x+5)=0

x=10or -5

x=10

two numbers 10&5

x=-5

two numbers is -5&0

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