The difference of two numbers is 4. If the difference of their recipro

1.	The difference of two numbers is 4. If the difference of their reciprocals is \(\frac{4}{21},\) find the numbers.
Answer» Let the numbers be ‘a’ and ‘b’. Given, difference of two numbers is 4 and difference of their reciprocals is \(\frac{4}{21}\) ⇒ 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

The difference of two numbers is 4. If the difference of their reciprocals is \(\frac{4}{21},\) find the numbers.

Answer»

Let the numbers be ‘a’ and ‘b’.

Given, difference of two numbers is 4 and difference of their reciprocals is \(\frac{4}{21}\)

⇒ 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