the difference of two numbers is 5 and the difference of their reciprocals is 1/10. find the no.s.....

plz show wid procedure.... answer is not comin..

Let the two numbers be *x* and *x* – 5.

According to the question,

⇒ *x* (*x* – 5) = 50

⇒ *x*^{2} – 5*x* – 50 = 0

⇒ *x*^{2} – 10*x +* 5*x* – 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.

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