The difference of two numbers is 4. If the difference of their reciprocals is , find the numbers.
Let the numbers be ‘a’ and ‘b’.
Given, difference of two numbers is 4 and difference of their reciprocals is
⇒ a – b = 4
⇒ a = b + 4
and 1/b – 1/a = 4/21
⇒ 1/(b + 4) – 1/b = -4/21
⇒ 21(b – b – 4) = -4(b2 + 4b)
⇒ b2 + 4b - 21 = 0
⇒ b2 + 7b – 3b – 21 = 0
⇒ b(b + 7) – 3(b + 7) = 0
⇒ (b – 3)(b + 7) = 0
⇒ b = 3, - 7
Numbers are , 3, 7 or -7, -3