If the product of three consecutive numbers is 64, then their mean proportional is-?
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let the 3 concecutive numbers be x, x+1 ,x+2
According to the question
(x) × (x+1) × (x+2)
64 = (x^2 + x) × (x+2)
64 = x^2 (x + 2) + x (x + 2)
64 = x^3 + 2x^2 + x^2 + 2x
64 = x^3 + 3x^2 + 2x
0 = (x^3 + 3x^2) + (2x - 64)
= x^2 (x+3) + 2 (x-32)
= (x^2 + 2) + (x + 3) + (x-32)
therefore
x = root -2. not possible
x = -3
x = 32
therefore x can be -3 or 32
According to the question
(x) × (x+1) × (x+2)
64 = (x^2 + x) × (x+2)
64 = x^2 (x + 2) + x (x + 2)
64 = x^3 + 2x^2 + x^2 + 2x
64 = x^3 + 3x^2 + 2x
0 = (x^3 + 3x^2) + (2x - 64)
= x^2 (x+3) + 2 (x-32)
= (x^2 + 2) + (x + 3) + (x-32)
therefore
x = root -2. not possible
x = -3
x = 32
therefore x can be -3 or 32
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