Permutations and Combinations

Permutations and Combinations

Question

The sum of three numbers in A.P. is 21 and the product of first and the third numbers exceeds the second number by 6, find the three numbers.

Answer

Let the three numbers in A.P. be a - d, a, a + d.
Since the sum of the number = 21

∴  a - d + a + a + d = 21                             or               3a = 21
or                         a = 7
Since the product of first and the third numbers exceeds the second number by 6.

∴    (a - d) (a + d) = a + 6             or            space space straight a squared space minus space straight d squared space equals space straight a space plus space 6
or            7 squared minus straight d squared space equals space 7 space plus space 6          or              49 - 13 = space space space straight d squared
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#6 {main}</pre>                or                  straight d space equals space plus-or-minus space 6
When d = 6, numbers are 7 - 6, 7, 7 + 6
or                                 1, 7 , 13
When d = -6, numbers are 7 + 6, 7, 7 - 6
or                                  13, 7, 1

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