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if a,b,c,d,e are distinct integers such that (8-a)(8-b)(8-c)(8-d)(8-e)=12 then find a+b+c+d+e

if a,b,c,d,e are distinct integers such that (8-a)(8-b)(8-c)(8-d)(8-e)=12 then find a+b+c+d+e

Grade:12

1 Answers

Arun
25750 Points
5 years ago
Dear Priya
 
Factors of 12 = 2 * 2 * 3 * 1 *1
For distinct factors
12 = 2 * (-2) * 3 * 1 * (-1)
Hence 
8 -a = 2 
8 - b = -2
8 -c = 3
8 - d = -1
8 -e = 1
Hence on adding
40 -(a+b+c+d+e) = 3

Hence
a+b+c +d +e = 37

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