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Example 18 - If AM and GM of a, b are 10, 8 - Chapter 9 - AM and GM (Arithmetic Mean And Geometric mean)

  1. Chapter 9 Class 11 Sequences and Series
  2. Serial order wise
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Example 18 If A.M. and G.M. of two positive numbers a and b are 10 and 8, respectively, find the numbers. Now we have a + b = 20 โ€ฆ(1) ab = 64 โ€ฆ(2) From (2) ab = 64 a = 64/๐‘ Putting a = 64/๐‘ in (1) a + b = 20 64/๐‘ + b = 20 (64 + ๐‘2)/๐‘ = 20 64 + b2 = 20b b2 โ€“ 20b + 64 = 0 b(b โ€“ 16) โ€“ 4(b โ€“ 16) = 0 (b โ€“ 4)(b โ€“ 16) = 0 b โ€“ 4 = 0 or b โ€“ 16 = 0 b = 4 or b = 16 Hence the numbers are a = 4, b = 16 or b = 4, a = 16

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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