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The difference of two natural number is 5 and the difference of their reciprocals is 1 / 10. Find the numbers.
Putting the value of x from equation (i) in equation (ii), we get
(y+5)y=50
⇒ y2+5y−50=0
⇒ y2+10y−5y−50=0
⇒ y(y+10)–5(y+10)=0
⇒ (y−5)(y+10)=0
⇒ y = 5 or -10
As y is a natural number, therefore y = 5
Other natural number = y + 5 = 5 + 5 = 10
Thus, the two natural numbers are 5 and 10.
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