Asked by Theo
The product of three consecutive odd integers reduced by 23 is 99 less than the cube of the sum of the smallest number and 2. Compute the mean of the three integers.
Answers
Answered by
Reiny
let the 3 consecutive numbers be
x-2, x and x+2
(x-2)(x)(x+2) - 23 = (x-2 + 2)^3 - 99
x(x^2 - 4) - 23 = x^3 - 99
x^3 - 4x = x^3 - 99 + 23
-4x = -76
x = 19
the three numbers are 17, 19, and 21
and their mean is 19
x-2, x and x+2
(x-2)(x)(x+2) - 23 = (x-2 + 2)^3 - 99
x(x^2 - 4) - 23 = x^3 - 99
x^3 - 4x = x^3 - 99 + 23
-4x = -76
x = 19
the three numbers are 17, 19, and 21
and their mean is 19
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