If AM and GM of two positive numbers a and b are 10 and 8 respectively, find the numbers.

Question

Philoid · Accepted Answer

⇒

⇒ GM = √ab

Given AM = 10, GM = 8.

⇒

⇒ a + b = 20

⇒ a = 20–b

⇒

⇒ 20b – b² = 64

⇒ b² – 20b + 64 = 0

⇒ b² – 16b – 4b + 64 = 0

⇒ b(b – 16) – 4(b – 16) = 0

⇒ b = 4 or b = 16

⇒ If b = 4 then a = 16

⇒ If b = 16 then a = 4.

Hence, the numbers are 4 and 16.