three numbers are in arithmetic progression.their sum is 18 and their product is 18. determine the three numbers.
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let the three numbers x,x+d,x+d+d
where d = common difference
x+x+d+x+d+d = 18
3x + 3d = 18
x + d = 6
x = 6 - d
x(x+d)(x+d+d) = 18
sub x = 6 - d
6 - d(6 - d + d)(6 - d + d + d) = 18
6-d(6)(6+d) = 18
(36-6d)×(36+6d) = 18
1296 - 36d^2 = 18
also, 72-2d^2 = 1
-2d^2 = 1-72 = -71
d^2 = -71/(-2) = 35.5
d = √35.5
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