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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 …(1) ab = 64 …(2) From (2) ab = 64 a = 64/𝑏 Putting a = 64/𝑏 in (1) a + b = 20 64/𝑏 + b = 20 (64 + 𝑏2)/𝑏 = 20 64 + b2 = 20b b2 – 20b + 64 = 0 b(b – 16) – 4(b – 16) = 0 (b – 4)(b – 16) = 0 b – 4 = 0 or b – 16 = 0 b = 4 or b = 16 Hence the numbers are a = 4, b = 16 or b = 4, a = 16

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