Q. 104.8( 6 Votes )
If AM and GM of two positive numbers a and b are 10 and 8 respectively, find the numbers.
⇒ 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.
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